Wednesday, August 29, 2007
Windows live recovery
Do you think windows live password can be recovered? Lets check it out here. Windows Live Password Recovery is the Windows Live password finder that instantly cracks and decrypts the Windows Live Messenger, MSN Messenger and Windows Messenger passwords stored on your computer. This tool is the ideal solution for those people who have a lot of accounts and so can't remember all of them. Like many bloggers, I have multiple accounts. But because of the security problems I can never use the same password in all the different accounts. This is where I need the help of some powerful software which can solve my problems. After a frantic search in the internet, I come across this site called http://www.windows-live-password-recovery.com. This site gives me the right software that I was dreaming to get. You can easily download this from the site. With the use of this software you don't need not to worry about passwords they have Windows Live Password Recovery system which keeps a copy of it in your own personal computer. What you need is to keep a regular back-up of the copy of encrypted passwords in your computer. Even in some situation, you can recover the passwords. But as I am very concerned about my passwords, I keep a regular back up. Nowadays, I don't spend my time too much in thinking of a new password as I know that the software would save my password. I don't need to even write the passwords myself. It automatically logs you in when you hit the name of the site. But you need to remember the master password for opening the software. So, just remember a single password, and you don't need to remember any other passwords.
Traveling New York
If you ask me what is the best thing that money can buy us, I would say that traveling to new and different parts of the world is probably the best thing that money can buy us. Everything is connected to form a one big chain and the glue is money but than when money leaves, information and communication picks up. People had money since money was invented and maybe they traveled too since ages but the way traveling has been made easier now, it must never have been so.
There is a long list of places I would like to go see if I ever won the lottery. I would like to see the UK and Australia and maybe take one of those jungle tours in Africa. I saw them doing that on the discovery channel. I would love to see the Rocky Mountains under a blanket of Snow. Plus all of the usual places like the Bahamas and Hawaii. Canada would be a really cool place to visit one of these days. I would also like to go to New York to see the height of the human civilization.
Traveling is easy nowadays.You can get many cheap flights. You can just dial a number, voice in the location and your proposed dates for travel and bingo, you get yourself booked on the joyride. There might be many such services on the internet but one such service is dialaflight.com. You can call the number 0870·416·0250, which is also mentioned on their website and check out the rates and book the flight then and there. You can search for flights to the cities across the world. From flights to New York to Tokyo, you name the city, you have it on their portal. So, by now you know where to look to if you are on for any travel.
That was a sponsored post.
There is a long list of places I would like to go see if I ever won the lottery. I would like to see the UK and Australia and maybe take one of those jungle tours in Africa. I saw them doing that on the discovery channel. I would love to see the Rocky Mountains under a blanket of Snow. Plus all of the usual places like the Bahamas and Hawaii. Canada would be a really cool place to visit one of these days. I would also like to go to New York to see the height of the human civilization.
Traveling is easy nowadays.You can get many cheap flights. You can just dial a number, voice in the location and your proposed dates for travel and bingo, you get yourself booked on the joyride. There might be many such services on the internet but one such service is dialaflight.com. You can call the number 0870·416·0250, which is also mentioned on their website and check out the rates and book the flight then and there. You can search for flights to the cities across the world. From flights to New York to Tokyo, you name the city, you have it on their portal. So, by now you know where to look to if you are on for any travel.
That was a sponsored post.
Mathematical notation
Most of the mathematical notation in use today was not invented until the 16th century.[10] Before that, mathematics was written out in words, a painstaking process that limited mathematical discovery. Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict syntax and encodes information that would be difficult to write in any other way.
Mathematical language also is hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Also confusing to beginners, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[11] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[12] Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[13]
Mathematical language also is hard for beginners. Words such as or and only have more precise meanings than in everyday speech. Also confusing to beginners, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".
Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow from axioms by means of systematic reasoning. This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.[11] The level of rigor expected in mathematics has varied over time: the Greeks expected detailed arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large computations are hard to verify, such proofs may not be sufficiently rigorous.[12] Axioms in traditional thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (sufficiently powerful) axiomatic system has undecidable formulas; and so a final axiomatization of mathematics is impossible. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.[13]
Friday, August 24, 2007
Get your choice of terrysfabrics
Curtains although introduced to keep out light and for privacy has become one the most focussed parts of interior designing now a days. By bringing about minute changes in the color and design of curtains the whole outlook of the building will be changed.I came across this site called http://www.terrysfabrics.co.uk/.Their range of ready made curtains are available in all colors and a variety of shades and designs at prices which will be in accordance with your budget.They also provide a number of curtain accessories like curtain poles ,eyelets,tab tops etc.Visit this site and check out the eye catching designs offered by them.
That was a paid post.
That was a paid post.
FERRARI and MERCEDES-BENZ set for bicycles
The makers of the luxury cars turn towards the luxury of the two wheeled kind. Whether it’s the four legged fuel driven beasts that zip past or the two legged muscle powered vehicles that speed by, the masters of transportation design constantly try to boost their brand equity. The latest car debuted from car makers Ferrari is Colnago. Commemorating the sixtieth anniversary of the brand, the bicycle is based on the colnago extreme power frame. Completely made in carbon fiber and assembled through lugs, it allows customization. Its Italian parentage can be seen from the stylish tricolor flag of
Italy featured in the bike. The fork made in carbon fiber gives reliability and safety. And Mercedes is not staying behind. They come up with three new sports bike. They have announced their participation in the competition of the 2007 bike collection. The technical and the functional features of new fitness and trekking bikes echo the ethos of the brand. The bold curves curves bring alive the Benz character, a clear reflection of the unmistakable styling from the Mercedes Benz Design Center in Sindelfingen. For the first time, the interplay of bold curves and straight lines grafts from the current design language of Mercedes-Benz cars finds way onto the muscle powered single-track vehicles. The core values of the Mercedes-Benz are integrated into the bicycle.
Italy featured in the bike. The fork made in carbon fiber gives reliability and safety. And Mercedes is not staying behind. They come up with three new sports bike. They have announced their participation in the competition of the 2007 bike collection. The technical and the functional features of new fitness and trekking bikes echo the ethos of the brand. The bold curves curves bring alive the Benz character, a clear reflection of the unmistakable styling from the Mercedes Benz Design Center in Sindelfingen. For the first time, the interplay of bold curves and straight lines grafts from the current design language of Mercedes-Benz cars finds way onto the muscle powered single-track vehicles. The core values of the Mercedes-Benz are integrated into the bicycle.
Thursday, August 23, 2007
Credit card dealings
Like everyone I am so interesting about credit card deal ,because some of them offer me a very exciting program. Some of them offer me cash back, free dining and others. There's nothing like some wonderful credit card love. Credit cards can be good, or they can be very, very bad. If you make your minimum payments, then a credit card can be a wonderful tool that can gather you a great credit score, which allows you to get those big loans that will pay for your house, car or boat. I own a few credit cards, and am always online looking for the next great credit card deal. I am Looking for low interest payments, a good APR for the past few days.
Fortunately for me I found a credit card deal which offers a lot of benefits for us. They gives free services on balance transfers (2.5% fee) until 1 August 2008 and bonus offer until 1 April 2009 on balance transfers debited to our account during October 2008 (2.5% fee).Since it also have a lower typical APR ,I think I shoud apply it in the earliest. Even though I have already got two, I can't miss this chance.
That was a paid review.
Fortunately for me I found a credit card deal which offers a lot of benefits for us. They gives free services on balance transfers (2.5% fee) until 1 August 2008 and bonus offer until 1 April 2009 on balance transfers debited to our account during October 2008 (2.5% fee).Since it also have a lower typical APR ,I think I shoud apply it in the earliest. Even though I have already got two, I can't miss this chance.
That was a paid review.
The Thokchom family
Doesn’t this sound like a hit movie or a hit novel. Well, its not actually. I am writing here some of my personal informations off the main theme of this blog. So, from where do I start? Let me start from this -that my surname is Thokchom and this Thokchom is a big surname in the whole of Manipur. There are other big surnames too, but still, Thokchom is included among some of the biggest surnames as far as I know. The Thokchom family comes under the Moirang yek or say clan. So Thokchom people are often found referring themselves as Moirangcha- the sons of Moirang. The first person who started to put this surname in his name was a decendent of Moirang clan, and hence Moirangcha. That is the brief history of Thokchom surname.
My village Nilakuthi has a small inhabitant of Thokchom family clustered in the Nilakuthi Maning Leikai. There is an annual meet of the thokchom family in different parts of Manipur. This type of practice is also common in other surnames too. But not all Thokchoms participate in it as again there are hundreds of division in a single surname to make the meet/feast feasible. We call this Chafu Kaiba or chaphu kaiba. I had participated in some of the feast and it is really a very good step taken up by the people of Manipur as it bring together all the brothers and sisters of distant relatives on a single spot on a single day. And every surname family has a puya or holy book which contains all the sons and wifes of every person belonging to the surname. So the ancestry can be easily traced back for anyone who is a Manipuri. Our Thokchom puya contains the brief story of the life of the founder, then his sons and daughter-in-laws and so and so. The only thing which I feel unsatisfied in it is the absence of the names of daughters in the list. But still, the wifes of male members are clearly given with their respective parental surnames. I believe that everyone in Manipur can be made related to each other by compiling all the puyas of every surname in Manipur. And lastly I am proud to be in the Thokchom family or being Moirangcha.
My village Nilakuthi has a small inhabitant of Thokchom family clustered in the Nilakuthi Maning Leikai. There is an annual meet of the thokchom family in different parts of Manipur. This type of practice is also common in other surnames too. But not all Thokchoms participate in it as again there are hundreds of division in a single surname to make the meet/feast feasible. We call this Chafu Kaiba or chaphu kaiba. I had participated in some of the feast and it is really a very good step taken up by the people of Manipur as it bring together all the brothers and sisters of distant relatives on a single spot on a single day. And every surname family has a puya or holy book which contains all the sons and wifes of every person belonging to the surname. So the ancestry can be easily traced back for anyone who is a Manipuri. Our Thokchom puya contains the brief story of the life of the founder, then his sons and daughter-in-laws and so and so. The only thing which I feel unsatisfied in it is the absence of the names of daughters in the list. But still, the wifes of male members are clearly given with their respective parental surnames. I believe that everyone in Manipur can be made related to each other by compiling all the puyas of every surname in Manipur. And lastly I am proud to be in the Thokchom family or being Moirangcha.
Monday, August 20, 2007
Visit Australia
If there is anyone who wants to know something about traveling to Melbourne, then I am here to say something I know about It. Melbourne is a great tourist spot in Australia. You would always want to visit it once you visit the place. It is such a great tourist spot for many tourists around the world.
Melbourne also known as Australia’s "sporting and cultural capital" has great shopping areas that sell locally designed clothes to high end boutiques, renowned dining and major art and musical extravaganzas. It is a great place to visit and there are ample cheap Melbourne hotel for your choosing. You can also find luxurious hotels there ranging from 3 star to 5 star hotels. The food is also found plenty with all continental foods.
In the city, the nightlife is vibrant with a wide range of trendy clubs and bars as well as theaters and cinemas. There are also cheap hotels in Melbourne in the city center with different options to suit various style and budget. You need not to worry about the accommodations as you will always get a hotel whether it is cheap or costly. Costlier hotels has many extra luxurious items and services. The services they provide are one of the best in Australia. In the nearby area, you also should not miss to see Sydney. There are also many Sydney Hotel in the city. Also the Darling Harbour Hotel is famous for the services they provide in Australia. Besides these hotels there are many other good hotels which can be booked through www.cheaperthanhotels.com.
Melbourne also known as Australia’s "sporting and cultural capital" has great shopping areas that sell locally designed clothes to high end boutiques, renowned dining and major art and musical extravaganzas. It is a great place to visit and there are ample cheap Melbourne hotel for your choosing. You can also find luxurious hotels there ranging from 3 star to 5 star hotels. The food is also found plenty with all continental foods.
In the city, the nightlife is vibrant with a wide range of trendy clubs and bars as well as theaters and cinemas. There are also cheap hotels in Melbourne in the city center with different options to suit various style and budget. You need not to worry about the accommodations as you will always get a hotel whether it is cheap or costly. Costlier hotels has many extra luxurious items and services. The services they provide are one of the best in Australia. In the nearby area, you also should not miss to see Sydney. There are also many Sydney Hotel in the city. Also the Darling Harbour Hotel is famous for the services they provide in Australia. Besides these hotels there are many other good hotels which can be booked through www.cheaperthanhotels.com.
Saturday, August 18, 2007
HIV rapid home test
HIV has so far no perfect cure once the person starts giving AIDS symptoms. But it can easily be prevented if we follow certain rules. Those rules are simple and if followed, one will not have HIV in his body. Those rules are known to all, thanks to the alarmingly increasing media. At least we know that we should never share syringes, or copulate with an infected person etc. But what about those who have shared syringes or done something that might possibly bring the virus to their body. There are many tests available for them. Most of them are done in government hospitals. HIV positive can still live longer if diagnosed in time. The person can get necessary potions and medicines if he or she is diagnosed before the person suffers from AIDS. But who would want to be an AIDS patient, who would want to show himself to everyone that he is testing for HIV infection. It is like a taboo subject in many parts of the world. Even in big cities, the subject is still a taboo. What yo do if you suspect that you may be getting infection and still you don't want to show it to others that you suspect yourself. You would definitely not want to go for the government hospital for fear of being seen by others. Obviously you would be looking for other source where you would get the chance to test and get medical attention without the notice of your neighbors. The site called http://www.tkno.org gives this rare opportunity to all such victims. You can get their medical attention with the expenditure of a minimum balance of $150. You can have the choice to get yourself checked of the infection at night at daytime. It depends on your choice.
Circle
A circle is a geometrical curve which is equidistant from a fixed point called center of the circle. Many natural objects take the form of circle. The orbit of the earth is also circular.
some facts about circle.
It is equidistant from a point called center.
The circumference of the circle is given by 2*r*pie.
The area of the circle is given by pie*r*r.
A line joining 2 parts of the circle is called chord.
A part of the circle is called arc.
some facts about circle.
It is equidistant from a point called center.
The circumference of the circle is given by 2*r*pie.
The area of the circle is given by pie*r*r.
A line joining 2 parts of the circle is called chord.
A part of the circle is called arc.
Friday, August 17, 2007
Flight to Australia
The following is a sponsored review.
When you talk about places you want to visit, there is so much places that one may want to see and stay there. But if you ask me the same question now, I would answer Australia. In fact, Australia is my dream destination. I have always wondered of spending Holidays in Australia. I want to pay a visit to this country at least before I die. However till now I have to find a good and cheap travel package to go for this country. The things which attract me to Australia are many and varied. It has a wide range of both natural and man made tourist attractions. The natural beauty and the artificial beauty seems to merge carefully with each other in Australia.
If I am going to Australia, I would need to look for Cheap Flights as well as cheap hotel in Australia, be it Sydney Hotel, hotel in Melbourne or hotel in Brisbane. It does depend where I would go either Sydney, Melbourne, Brisbane or other places. But I think I would visit all of them at once as I don’t think I would go there often. There are many things that we can do there. We can go for boating, catch the light rail, go for surfing etc. They also have very nice spot for shopping and entertainment over all the main cities.
Normally we don't get cheap flights to Australia. But the site called http://www.dialaflight.com/flights/australia/ allows me to book for flights for Australia at a fairly cheap price. This is a great offer as far as I am concern as there are many people like me who don't want to spend too much money in flight yet have the desire to go for holidaying.
When you talk about places you want to visit, there is so much places that one may want to see and stay there. But if you ask me the same question now, I would answer Australia. In fact, Australia is my dream destination. I have always wondered of spending Holidays in Australia. I want to pay a visit to this country at least before I die. However till now I have to find a good and cheap travel package to go for this country. The things which attract me to Australia are many and varied. It has a wide range of both natural and man made tourist attractions. The natural beauty and the artificial beauty seems to merge carefully with each other in Australia.
If I am going to Australia, I would need to look for Cheap Flights as well as cheap hotel in Australia, be it Sydney Hotel, hotel in Melbourne or hotel in Brisbane. It does depend where I would go either Sydney, Melbourne, Brisbane or other places. But I think I would visit all of them at once as I don’t think I would go there often. There are many things that we can do there. We can go for boating, catch the light rail, go for surfing etc. They also have very nice spot for shopping and entertainment over all the main cities.
Normally we don't get cheap flights to Australia. But the site called http://www.dialaflight.com/flights/australia/ allows me to book for flights for Australia at a fairly cheap price. This is a great offer as far as I am concern as there are many people like me who don't want to spend too much money in flight yet have the desire to go for holidaying.
Triangle
What is a triangle?
Tri stands for 3 ; and combine with angle, we get 3 angles.
That is a figure with 3 angles. Of course the figure should be closed figure. So 3 angles is possible in a 3 sided closed figure and so a triangle is a three sided closed figure.
A triangle has 3 angle.
A triangle has 3 sides.
The sum of the 3 angles is 180 degree.
Equilateral triangle has all its sides equal.
Isosceles triangle has 2 of its sides equal.
A right triangle has a 90 degree angle.
If one of the angles is more than 90 degree, it is called an obtuse angle.
Tri stands for 3 ; and combine with angle, we get 3 angles.
That is a figure with 3 angles. Of course the figure should be closed figure. So 3 angles is possible in a 3 sided closed figure and so a triangle is a three sided closed figure.
A triangle has 3 angle.
A triangle has 3 sides.
The sum of the 3 angles is 180 degree.
Equilateral triangle has all its sides equal.
Isosceles triangle has 2 of its sides equal.
A right triangle has a 90 degree angle.
If one of the angles is more than 90 degree, it is called an obtuse angle.
Thursday, August 16, 2007
Donate useless cloths
All of us have old and unused clothings. But, what do we usually do with old and unused clothes? We throw it most of the times or used it in some cleaning purposes. But that is not productive if we remember that there are numerous people who are not rich enough to buy even their necessary clothing. Again we find in many occasions where clothes bought for children do not fit any more even though the clothings are not bad. In such cases, I advise you, please dont just throw away the clothes. There are thousands of people, who can reuse them. You may feel surprise to hear this. But it is true. I have found a site called http://blog.planetaid.org/ which works in collecting cloths for the needy peoples. Planet Aid is an mission, which helps the needy people get their basic share of clothings. This site is doing a selfless role that we can't even think of. I like this way of helping the people. Your contribution can really, make a big change. The donor also don't need to think for a second thought to donate a useless cloth. In this way, it is a great success.
That was a sponsored review.
That was a sponsored review.
Wednesday, August 15, 2007
Knowing stock market
We all know that stock market can get us really fat money. But it is not easy to consistently make money in the stock market if you are not so good at it. Knowledge about market trends and timing are some of the key elements all stock traders should possess. Perfecting in the knowledge of such important elements need profound knowledge, practice and experience. It is not easy to be able to grasp and master the concept of these key elements and put it to practice effectively. Personally I have very little knowledge for stock market. I think I need to learn some from an expert. But they would demand big money. So the best seems to be from a website dedicated in such marketing topic.
I found such a site called http://www.wizetradeblog.com. It is a new stock market and securities website offering advanced stock trading tools and news updates. Their proprietary stock trading software, Wizetrade, is a powerful program enabling traders to conduct stock market analysis and quickly chart potential entry and exit points for any stocks. In addition, this blog has consistent product updates information and is filled with interesting information, videos and pictures of events happening in the securities world. You would benefit greatly if you are a regular visitor of the site.
That was a sponsored review.
I found such a site called http://www.wizetradeblog.com. It is a new stock market and securities website offering advanced stock trading tools and news updates. Their proprietary stock trading software, Wizetrade, is a powerful program enabling traders to conduct stock market analysis and quickly chart potential entry and exit points for any stocks. In addition, this blog has consistent product updates information and is filled with interesting information, videos and pictures of events happening in the securities world. You would benefit greatly if you are a regular visitor of the site.
That was a sponsored review.
How to Multiply by 11
How do we multiply by eleven easily?
First we will try this by writing the answer backwards.
So, when always multiplying a large number by 11, the last number will always be the last number of the sum we are multiplying.
Let me explain.
176 is the number we are multiplying.
So the last number in out answer will be 6. If the sum was 143 the last number in our answer would be 3
First we will try this by writing the answer backwards.
So, when always multiplying a large number by 11, the last number will always be the last number of the sum we are multiplying.
Let me explain.
176 is the number we are multiplying.
So the last number in out answer will be 6. If the sum was 143 the last number in our answer would be 3
Tuesday, August 14, 2007
sign up form for advertiser
Monday, August 13, 2007
Disclosure Policy
This policy is valid from 13 August 2007
For questions about this blog, please contact kritithok@yahoo.com.
This blog accepts forms of cash advertising, sponsorship, paid insertions or other forms of compensation.
The compensation received may influence the advertising content, topics or posts made in this blog. That content, advertising space or post may not always be identified as paid or sponsored content.
The owner(s) of this blog is compensated to provide opinion on products, services, websites and various other topics. Even though the owner(s) of this blog receives compensation for our posts or advertisements, we always give our honest opinions, findings, beliefs, or experiences on those topics or products. The views and opinions expressed on this blog are purely the bloggers' own. Any product claim, statistic, quote or other representation about a product or service should be verified with the manufacturer, provider or party in question.
This blog does contain content which might present a conflict of interest. This content may not always be identified.
To get your own policy, go to http://www.disclosurepolicy.org
For questions about this blog, please contact kritithok@yahoo.com.
This blog accepts forms of cash advertising, sponsorship, paid insertions or other forms of compensation.
The compensation received may influence the advertising content, topics or posts made in this blog. That content, advertising space or post may not always be identified as paid or sponsored content.
The owner(s) of this blog is compensated to provide opinion on products, services, websites and various other topics. Even though the owner(s) of this blog receives compensation for our posts or advertisements, we always give our honest opinions, findings, beliefs, or experiences on those topics or products. The views and opinions expressed on this blog are purely the bloggers' own. Any product claim, statistic, quote or other representation about a product or service should be verified with the manufacturer, provider or party in question.
This blog does contain content which might present a conflict of interest. This content may not always be identified.
To get your own policy, go to http://www.disclosurepolicy.org
dclickads- a solution for advertiser and webmaster
There are many sites coming up with nice attractive offers for bloggers and advertiser alike. Among all these sites there are only a few which are successful and are trusty. There are many sites which claims of such offers to advertisers and bloggers but many of them end up with no or little functionality. I come across a site which gives such a great offer to both the advertisers and bloggers. The name of the site is www.Dclickads.com, which is a new advertising network for both webmasters to increase advertising revenue and publishers to increase traffic and clicks. In this site bloggers would be paid for clicks in the ads they put up in their site by the sponsor or the advertiser. So, bloggers earn money from this click and advertiser gets traffic from these clicks. Through this site you are able to buy and sell text links, graphic banner ads, and embedded inline ads.
The best part that I like about Dclickads is that it’s completely free to register, and you get money in time in return of your assignment for the advertiser. Also, you can pick between PPC (Pay Per Click) or PPI (Pay Per Impression) so that you are given the option to advertise any ads for a specific time frame as per your decision.
Personally I like the site. It works in the same manner as google adsense. But the prospect is better in this site. You can take out the sum at any time you want as money is sent directly to you through your paypal account.
The best part that I like about Dclickads is that it’s completely free to register, and you get money in time in return of your assignment for the advertiser. Also, you can pick between PPC (Pay Per Click) or PPI (Pay Per Impression) so that you are given the option to advertise any ads for a specific time frame as per your decision.
Personally I like the site. It works in the same manner as google adsense. But the prospect is better in this site. You can take out the sum at any time you want as money is sent directly to you through your paypal account.
About Discountclick
I have come across a site. The name of the site is http://www.discountclick.com/. Discount Click is a company that provides online marketing services that range from basic do-it-yourself options to more inclusive packages where everything is taken care of for you. The company is unique because it offers free advice so that you can learn about SEO and try out some techniques on your own. Many other companies that offer online marketing services will not provide free information because they feel it will cut down on their business. If you have the time and the patience to learn SEO and SE marketing, then this information will be very valuable to you.
If you don’t understand Search Engine Optimization (SEO) or you just don’t have the time to do your own optimization, Discount Click also offers a wide range of paid SEO Marketing services that are organic in nature. The company stays away from black hat and unethical SEO tactics that may work temporarily, but will almost certainly get you penalized or banned from the search engines later on down the road. Discount Click can help you increase your SEO rankings with a number of services that include link building campaigns, pay per click campaign managements, on-page optimization, and analysis of the best keywords for your target market.
If you don’t understand Search Engine Optimization (SEO) or you just don’t have the time to do your own optimization, Discount Click also offers a wide range of paid SEO Marketing services that are organic in nature. The company stays away from black hat and unethical SEO tactics that may work temporarily, but will almost certainly get you penalized or banned from the search engines later on down the road. Discount Click can help you increase your SEO rankings with a number of services that include link building campaigns, pay per click campaign managements, on-page optimization, and analysis of the best keywords for your target market.
Sunday, August 12, 2007
Be a lucky bidder
Are you a lucky person when it comes to bidding or in lottery. I am never a good bidder and my luck will also never allow me to win a lottery or a bid. But I found something interesting. You will surely get surprised to hear this. I have found a site which is very interesting. You would feel like visiting it everyday. This site allows you to bid a product for free to get exciting cash prize and free gifts. And the interesting thing is, you win if you are the lowest bidder. It is more like a game than anything. And if you are lucky , then you win. At this site, the bidder with the lowest bid is the one to win the auction. It’s just like Ebay, but except the roles are reverse. Which is kind of interesting to me. The “How To” page (see How To Play) explains things a little more in depth. But you are to be lucky enough to make your bid unique. For example if more than 1 person bid 1 cent for the prize, 1 dollar is no longer the lowest bid. 2 cents is now the lowest bid. But again out of the million bidders, if some another person bid 2 cent it is again an invalid bid. So you are to be so lucky to choose that unique minimum bid to win the prize. It is a great fun.Simply put, Bid4prizes is an Sweepstake site that offers prizes to the lowest bidder at the end of the auction. The prizes Apple I-Phone’s, HDTV’s, Designer Bags, SCION XB’s and even Cash Prizes.Some of the current auctions still going on are on ipod, car, bike etc. I am waiting for the result for my bid in Ipod and $500 dollar cash prize. I would love to have that. Easy money for a nice long vacation with my friends. So, visit the site now and check your luck.
Basics of virtual server
What is a virtual server? You may say that it is a PC which acts like a server for you and your site as in localhost. But before we go further on, let us see the basic things first. A computer network is a group of computers that are connected together to share resources. A standalone home PC is not connected in a network. It cannot share computer resources directly. It is not secured because data on the local hard disk storage is easily accessible by others, unless you lock them securely in a secluded room. A LAN is a group of computers in close proximity that are connected together to share resources. Generally, it consists of at least one Server and many clients PCs. Its network users can communicate to each other via the network resources such as hard-disk space, data files, application programs and laser printer. Network operating System is system software that runs on the server to manage and maintain its users and controls the uses of all network resources.
A Network Administrator is entrusted to control the access rights to all the shared resources. He creates and maintains the network user accounts, and defines users access rights. There can be many other special types of servers connected in a network for users to use. For examples, database serves , World Wide-Web servers, Lotus Notes Work flow servers and Virtual Servers etc.
A computer network allows Centralized Management of their computers, users and resources. The network administrator, for instance, can organize all network users by workgroups, then assign access rights control by groups. The backup of data can also be done in one central location, while the upgrading of shared software can also be much easier. Virtual Servers have the advantage of allowing webmasters to go beyond shared hosting by having full access to a virtual server to install tools & utilities to create their sites. Whether you are a webmaster, developers, technologists, doing businesses or just a consumer, there are several Dedicated Virtual Server Plans which will suit your needs.
A Network Administrator is entrusted to control the access rights to all the shared resources. He creates and maintains the network user accounts, and defines users access rights. There can be many other special types of servers connected in a network for users to use. For examples, database serves , World Wide-Web servers, Lotus Notes Work flow servers and Virtual Servers etc.
A computer network allows Centralized Management of their computers, users and resources. The network administrator, for instance, can organize all network users by workgroups, then assign access rights control by groups. The backup of data can also be done in one central location, while the upgrading of shared software can also be much easier. Virtual Servers have the advantage of allowing webmasters to go beyond shared hosting by having full access to a virtual server to install tools & utilities to create their sites. Whether you are a webmaster, developers, technologists, doing businesses or just a consumer, there are several Dedicated Virtual Server Plans which will suit your needs.
Friday, August 10, 2007
Solving ortho related problems
Many people are affected by bone related pains and injuries. I give here a valuable information for such patients. Anyone seeking an orthopaedic doctor for medical treatment for knee and total hip replacement surgery and other ortho related problems are gretly in need of a visit to Gustafson Orthopaedics. The practice is headed by a board-certified orthopaedic surgeon, Dr Allen Gustafson himself, who is renowned for his experience, skill and accomplishment in joint replacement and reconstruction. The center also provides the following services:
Thorough evaluation and accurate diagnosis of joint pain
Effective treatment recommendations
Patient education resources
Expert surgical intervention, if needed
A complete recovery program
More details about hips and knees replacements, arthritis and the safety of such surgery, can be found in the FAQ section. You can also contact them if you have more questions. For more information about Gustafson Orthopaedics, you can visit its official website at www.gustafsonortho.com
That was a sponsored review.
Thorough evaluation and accurate diagnosis of joint pain
Effective treatment recommendations
Patient education resources
Expert surgical intervention, if needed
A complete recovery program
More details about hips and knees replacements, arthritis and the safety of such surgery, can be found in the FAQ section. You can also contact them if you have more questions. For more information about Gustafson Orthopaedics, you can visit its official website at www.gustafsonortho.com
That was a sponsored review.
Fibonacci sequence
Many of us have heard about Fibonacci sequence. Don't get yourself alarmed at the mention of the words. It is a very simple and easy sequence.
1 1 2 3 5 8 13 21 34 55 ................
What do you see in the sequence?
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
and so on.
So the trick is go on adding the successive terms to get the next term. Isn't it easy?
1 1 2 3 5 8 13 21 34 55 ................
What do you see in the sequence?
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
and so on.
So the trick is go on adding the successive terms to get the next term. Isn't it easy?
Promoting business through buildasign.com
Ever thought of promoting your site? If yes, what do you do. Like many people, When you are promoting your business you use every possible means available to you. This includes advertising you business and products in car plates as stickers and cars. I'm pretty sure everyone has seen window decals and bumper stickers. The problem with those things is that they are difficult to lay flat and even more difficult to remove.
It is not hard to find a solution for them. We can opt for magnetic Signs for your car. BuildASign.com can help you design your custom magnetic sign quickly and affordable. It is a very good site for designing, ordering, customizing and everything related with magnetic signs in a few minutes.You can design all those Banners, Magnetic signs, Parking Signs and even Yard Signs. BuildASign.com can help you with all of your immediate needs. All at great prices and easy clicks.
That was a sponsored review.
It is not hard to find a solution for them. We can opt for magnetic Signs for your car. BuildASign.com can help you design your custom magnetic sign quickly and affordable. It is a very good site for designing, ordering, customizing and everything related with magnetic signs in a few minutes.You can design all those Banners, Magnetic signs, Parking Signs and even Yard Signs. BuildASign.com can help you with all of your immediate needs. All at great prices and easy clicks.
That was a sponsored review.
Thursday, August 09, 2007
Multiply by 9
Finger Math: 9X Rule
To multiply by 9,try this:
(1) Spread your two hands out and place them on a desk or table in front of you.
(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.
(3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.
This works for anything up to 9x10!
To multiply by 9,try this:
(1) Spread your two hands out and place them on a desk or table in front of you.
(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.
(3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.
This works for anything up to 9x10!
Online American Fantasy Football League
we all like football in some way or another. We might not all watch every game that’s on, but everyone has a place in their heart for the game of champions. American Football is a great game, one of the games that only great and skillful players play. I also play football though I am not so good at it; I am very fond of watching American Football too. The clash between two teams, those fights and tackles are really very entertaining. Though many people don’t play American Football, they still can find a way to earn through it. There is an online site AFFL.com which is very interesting for all. After joining by filling up a fantasy football online registration form, you can compete and win big prizes. AFFL is the elite, high-class place to showcase your skills for a chance to win huge prizes. There are 5 levels of play which you can check out here. You can even join multiple levels once you feel that you have enough confidence. There are lots of prizes in different category to be won.
The site lets you create your own fantasy team and follow it throughout the season. I personally love creating these fantasy teams, but never end up doing to well compared to all my friends in my league.I recommend you guys all check out fantasy football online and see if you can make a better team than me.So, hurry up and fill up the fantasy form, make your fantasy football team and win lots of money.
That was a sponsored review.
The site lets you create your own fantasy team and follow it throughout the season. I personally love creating these fantasy teams, but never end up doing to well compared to all my friends in my league.I recommend you guys all check out fantasy football online and see if you can make a better team than me.So, hurry up and fill up the fantasy form, make your fantasy football team and win lots of money.
That was a sponsored review.
Inspiration for mathematics
Mathematics arises wherever there are difficult problems that involve quantity, structure, space, or change. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. Newton was one of the infinitesimal calculus inventors, Feynman invented the Feynman path integral using a combination of reasoning and physical insight, and today's string theory also inspires new mathematics. Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. The remarkable fact that even the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics."
As in most areas of study, the explosion of knowledge in the scientific age has led to specialization in mathematics. One major distinction is between pure mathematics and applied mathematics. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. Mathematicans often strive to find proofs of theorems that are particularly elegant, a quest Paul Erdős often referred to as finding proofs from "The Book" in which God had written down his favorite proofs. The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.
As in most areas of study, the explosion of knowledge in the scientific age has led to specialization in mathematics. One major distinction is between pure mathematics and applied mathematics. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science.
For those who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty in a simple and elegant proof, such as Euclid's proof that there are infinitely many prime numbers, and in an elegant numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. Mathematicans often strive to find proofs of theorems that are particularly elegant, a quest Paul Erdős often referred to as finding proofs from "The Book" in which God had written down his favorite proofs. The popularity of recreational mathematics is another sign of the pleasure many find in solving mathematical questions.
The world of Payperpost
I heard that some sites are offering paid service to the bloggers. I was not so sure at the first time. Payperpost was the first site I heard which give paid service. I heard about it from my close friend who was always busy in internet. Then I registered an account in it. I read the full account of what was going on inside the site. I also met some friends from forums which really helped me in giving real advices so that I can get my blog accepted in payperpost. I tried hard to get some real value content posts in my blog for 2 months again before registering my blog to Payperpost. I feared that if I was too hasty, I may get rejected. Well, that 2 month's hard work pays at last. My blog was accepted. I was so happy to complete my first assignment. I wanted to take even more opportunities, but it was limited to opportunities per day. Well, that system is good as it then checks even flow of pays to all its members. After joining this site, I learnt that the service payperpost is providing is not only to the bloggers but to the advertisers as well. That solved my curiosity why the site is willing to offer us paid post. Well, the idea is good and it makes both the bloggers and advertiser happy. Bloggers need not search for advertiser and advertiser need not search for bloggers. It is a common platform for both the sides. I have already done two assignments and this is the third one. If I go on like this, I may get at least $150 per month. $150 per month would be a nice thing for me. I could go for more time with my girl friend in parties. But first of all, I would buy a nice mobile from the money I get from payperpost. That would be really nice and the mobile would remain as a souvenir for the first income from payperpost.
The history of mathematics
The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges have something in common was a breakthrough in human thought. In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time — days, seasons, years. Arithmetic (addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to knowledge of geometry.
Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse.
From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs
Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse.
From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs
Wednesday, August 08, 2007
Hotel reservations
Are you planning to go for vacations? Visit HotelReservations.com. I like traveling so much and I want to be sure that each time I am going somewhere I made the best choice. I need to know that I choose the best hotel and flight in the best -cheapest- price. This is not easy; if you travel you know it, so I spend a few hours each time I want to make a trip, trying to find out the best destination. I have tried many sites, but recently I found HotelReservations.com which I think is one of the best. You can get Hotel Reservations easily and cheap through this site.
First of all it is a very user-friendly site. Its navigation is simple and you can find everything you want in just a few seconds. You can choose to search by the standard form, filling in all the info, or you can click on a part of the US or world you would like to visit. It offers more than 70,000 properties worldwide, so it's almost impossible not to find what you are looking for. Also, if you are planning a group event like a wedding, business event, sports team travel or any other special occasion, the group department can help you with requests of 9 or more hotel rooms. There is an easy to fill out form online or you can again call a convenient toll free number 7 days a week to have a specialist personally help you book hotels worldwide.
What I liked most? Their rates and the Special Internet Price Guarantee. What is that? According to the guarantee, if there is a lower rate available for the same dates and same hotel that you’ve booked, you can lodge a request within 24 hours, and your booking may be rebated to match the lower rate or reservations may be canceled. That might come as an advantage. This guarantee is enough, I think, to understand that the rates are extremely competitive, from hotel rates to airfares to car rentals, and there is a savings of up to 70%. Isn't this really interesting. I bet you would not get such offers easily in any of the sites available in the internet.
That was a sponsored review.
First of all it is a very user-friendly site. Its navigation is simple and you can find everything you want in just a few seconds. You can choose to search by the standard form, filling in all the info, or you can click on a part of the US or world you would like to visit. It offers more than 70,000 properties worldwide, so it's almost impossible not to find what you are looking for. Also, if you are planning a group event like a wedding, business event, sports team travel or any other special occasion, the group department can help you with requests of 9 or more hotel rooms. There is an easy to fill out form online or you can again call a convenient toll free number 7 days a week to have a specialist personally help you book hotels worldwide.
What I liked most? Their rates and the Special Internet Price Guarantee. What is that? According to the guarantee, if there is a lower rate available for the same dates and same hotel that you’ve booked, you can lodge a request within 24 hours, and your booking may be rebated to match the lower rate or reservations may be canceled. That might come as an advantage. This guarantee is enough, I think, to understand that the rates are extremely competitive, from hotel rates to airfares to car rentals, and there is a savings of up to 70%. Isn't this really interesting. I bet you would not get such offers easily in any of the sites available in the internet.
That was a sponsored review.
Eleven times
Times Eleven
The eleven times table has always been very easy to learn up to 9 x 11. Here's a way of multiplying large numbers by 11 too:
Example:
Q. What is 324 x 11 ?
A. Write down the first digit ... 3
.......Add the first and second digits ... 3 + 2 = 5
.......Add the second and third digits .. 2 + 4 = 6
.......Write down the last digit ........... 4
The answer is 3564.
Try it yourself ... multiply 543 by 11
Do you know why it works?
Does it work for all three digit numbers?
The eleven times table has always been very easy to learn up to 9 x 11. Here's a way of multiplying large numbers by 11 too:
Example:
Q. What is 324 x 11 ?
A. Write down the first digit ... 3
.......Add the first and second digits ... 3 + 2 = 5
.......Add the second and third digits .. 2 + 4 = 6
.......Write down the last digit ........... 4
The answer is 3564.
Try it yourself ... multiply 543 by 11
Do you know why it works?
Does it work for all three digit numbers?
Multiply Up to 20X20 In Your Head
In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.
I will assume that you know your multiplication table reasonably well up to 10x10.
Try this:
* Take 15 x 13 for an example.
* Always place the larger number of the two on top in your mind.
* Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
* First add 15 + 3 = 18
* Add a zero behind it (multiply by 10) to get 180.
* Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
* Add 180 + 15 = 195.
That is It! Wasn't that easy? Practice it on paper first!
I will assume that you know your multiplication table reasonably well up to 10x10.
Try this:
* Take 15 x 13 for an example.
* Always place the larger number of the two on top in your mind.
* Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
* First add 15 + 3 = 18
* Add a zero behind it (multiply by 10) to get 180.
* Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
* Add 180 + 15 = 195.
That is It! Wasn't that easy? Practice it on paper first!
Coupon chief
Before I start with,let me first ask you a question. Do you ever get tired of collecting discount cards inside your wallet, or cutting coupons from newspapers and magazines? Coupon Chief is the answer for all your problems. Not only is it a one-stop shop for discounts, coupons and deals, but it is also available online. And now Halloween is near that I have got many things in my mind to do and buy. I will be be buying toys for my cousin sister through the site.
The Coupon Chief website has three tabs for coupons, categories and stores. It has 22 categories available, with each category covering more than 4 web merchants. This means that thousands of coupon and discount offers are updated everyday. Some of the merchant like Target offering USD$5 off USD$50, if you want to buy a computer I suggest Dell because you can get huge discount from them.
A notable part of the CouponChief.com is the list of expiring offers. In this case, consumers will not be confused by stale offers. On the other hand, a header link is available listing all new offers. The site also indicates the date of update so visitors will be sure that listed offers are always the latest.
With Coupon Chief, consumers will get discounts and a lot of perks without the hassles. It is more convenient for consumers to check for all discounts or deals present in the market from one source than to make a call or buy a newspaper or magazine. You can get huge discount for buying magazine at netMagazines and sure you will like them. So what are you waiting for, hurry up.
The Coupon Chief website has three tabs for coupons, categories and stores. It has 22 categories available, with each category covering more than 4 web merchants. This means that thousands of coupon and discount offers are updated everyday. Some of the merchant like Target offering USD$5 off USD$50, if you want to buy a computer I suggest Dell because you can get huge discount from them.
A notable part of the CouponChief.com is the list of expiring offers. In this case, consumers will not be confused by stale offers. On the other hand, a header link is available listing all new offers. The site also indicates the date of update so visitors will be sure that listed offers are always the latest.
With Coupon Chief, consumers will get discounts and a lot of perks without the hassles. It is more convenient for consumers to check for all discounts or deals present in the market from one source than to make a call or buy a newspaper or magazine. You can get huge discount for buying magazine at netMagazines and sure you will like them. So what are you waiting for, hurry up.
Sunday, August 05, 2007
Maths is not ugly
Maths is more than just a subject. Its is also an art. There are many people fully absorbed in the study of the subject. Anyway, I am not so good at it though.
Things I see with this numbers:
1 - supreme. There is only 1 Supreme God.
2 - pair. A couple. man and woman.
3 - trinity. Trinity of everything
4 - 4 legs, all animal and chair has 4 legs
5 - 5 pandavas. 5 fingers
Things I see with this numbers:
1 - supreme. There is only 1 Supreme God.
2 - pair. A couple. man and woman.
3 - trinity. Trinity of everything
4 - 4 legs, all animal and chair has 4 legs
5 - 5 pandavas. 5 fingers
Friday, August 03, 2007
The number 7
Let me tell some of the things aroud the world connected with the number 7.
1. There are 7 days a week.
2. There are 7 wonders in the world.
3. Snow White has 7 dwarfs.
4. Musical note has 7 notes ( sa is repeated twice to make 8).
5. Harry Potter Book has 7 parts.
1. There are 7 days a week.
2. There are 7 wonders in the world.
3. Snow White has 7 dwarfs.
4. Musical note has 7 notes ( sa is repeated twice to make 8).
5. Harry Potter Book has 7 parts.
Math myth
A related myth in mathematics, which we hear every so often, goes something like this: "Jobs were tight in the early 1970s and then the market improved. It's a cyclic business and the market will get better again soon." Many of us no longer have faith in this myth, for reasons we will explain below, and we believe that mathematics departments should reconsider their missions. In particular, they should consider "downsizing" their graduate programs and re-examine the education provided in graduate school so that it more closely fits the reality of what our graduates will be doing in the future. Some group I universities, such as the University of California at Berkeley and the University of Michigan, have already started this process.
Many long-term economic, political, academic, historical, and technical issues indicate that the current downturn in full-time tenured employment of new young mathematicians is not likely to be reversed in the next decade. Even though you are aware of them all individually, it may be useful to consider them in totality and ponder their impact on mathematics. Our purpose is to state our reasons for our views without claiming to own a crystal ball.
First, the abrupt end of the cold war eliminated many compelling requirements for advanced R&D along with the organizations and staff supporting weapons development. Sizable rollbacks now exist at national labs and high-tech aerospace, electronic and design companies which for decades welcomed and employed many mathematicians, engineers and scientists. Displaced, highly qualified, mid-career individuals are entering the civilian economy on both sides of the (former) iron curtain. For thousands of them, their option will be to compete with new graduates for teaching positions at all educational levels. Overall, this is a healthy development because mathematics has always been a world-wide activity that has largely ignored artificial national boundaries, but there's no denying the impact on the current and future U.S. job market.
Many long-term economic, political, academic, historical, and technical issues indicate that the current downturn in full-time tenured employment of new young mathematicians is not likely to be reversed in the next decade. Even though you are aware of them all individually, it may be useful to consider them in totality and ponder their impact on mathematics. Our purpose is to state our reasons for our views without claiming to own a crystal ball.
First, the abrupt end of the cold war eliminated many compelling requirements for advanced R&D along with the organizations and staff supporting weapons development. Sizable rollbacks now exist at national labs and high-tech aerospace, electronic and design companies which for decades welcomed and employed many mathematicians, engineers and scientists. Displaced, highly qualified, mid-career individuals are entering the civilian economy on both sides of the (former) iron curtain. For thousands of them, their option will be to compete with new graduates for teaching positions at all educational levels. Overall, this is a healthy development because mathematics has always been a world-wide activity that has largely ignored artificial national boundaries, but there's no denying the impact on the current and future U.S. job market.
Perfect numbers
What is a perfect number?
Perfect numbers are positive integers n such that
n==s(n),
(1)
where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently
sigma(n)==2n,
(2)
where sigma(n) is the divisor function (i.e., the sum of divisors of n including n itself). For example, the first few perfect numbers are 6, 28, 496, 8128, ... (Sloane's A000396), since
6 = 1+2+3
(3)
28 = 1+2+4+7+14
(4)
496 = 1+2+4+8+16+31+62+124+248,
(5)
etc. The first few perfect numbers P_n are summarized in the following table together with their corresponding indices p (see below).
n p_n P_n
1 2 6
2 3 28
3 5 496
4 7 8128
5 13 33550336
6 17 8589869056
7 19 137438691328
8 31 2305843008139952128
Perfect numbers were deemed to have important numerological properties by the ancients, and were extensively studied by the Greeks, including Euclid.
Perfect numbers are also intimately connected with a class of numbers known as Mersenne primes, which are prime numbers of the form M_p==2^p-1. This can be demonstrated by considering a perfect number P of the form P==q.2^(p-1) where q is prime. By definition of a perfect number P,
sigma(P)==2P.
(6)
Now note that there are special forms for the divisor function sigma(n)
sigma(q)==q+1
(7)
for n==q a prime, and
sigma(2^alpha)==2^(alpha+1)-1
(8)
for n==2^alpha. Combining these with the additional identity
sigma(p_1^(alpha_1)p_2^(alpha_2)...p_r^(alpha_r))==sigma(p_1^(alpha_1))sigma(p_2^(alpha_2))...sigma(p_r^(alpha_r)),
(9)
where n==p_1^(alpha_1)p_2^(alpha_2)...p_r^(alpha_r) is the prime factorization of n, gives
sigma(P) = sigma(q.2^(p-1))
(10)
= sigma(q)sigma(2^(p-1))
(11)
= (q+1)(2^p-1).
(12)
But sigma(P)==2P, so
(q+1)(2^p-1)==2q.2^(p-1)==q.2^p.
(13)
Solving for q then gives
q==2^p-1.
(14)
Therefore, if P is to be a perfect number, q must be of the form q==2^p-1. Defining M_p as a prime number of the form M_P=q==2^p-1, it then follows that
P_p==1/2(M_p+1)M_p==2^(p-1)(2^p-1)
(15)
is a perfect number, as stated in Proposition IX.36 of Euclid's Elements (Dickson 1957, p. 3; Dunham 1990).
While many of Euclid's successors implicitly assumed that all perfect numbers were of the form (15) (Dickson 1952, pp. 3-33), the precise statement that all even perfect numbers are of this form was first considered in a 1638 letter from Descartes to Mersenne (Dickson 2005, p. 12). Proof or disproof that Euclid's construction gives all possible even perfect numbers was proposed to Fermat in a 1658 letter from Frans van Schooten (Dickson 2005, p. 14). In a posthumous paper, Euler (Euler 1849) provided the first proof that Euclid's construction gives all possible even perfect numbers (Dickson 2005, p. 19).
It is not known if any odd perfect numbers exist, although numbers up to 10^(300) have been checked (Brent et al. 1991; Guy 1994, p. 44) without success.
All even perfect numbers P>6 are of the form
P==1+9T_n,
(16)
where T_n is a triangular number
T_n==1/2n(n+1)
(17)
such that n==8j+2 (Eaton 1995, 1996). In addition, all even perfect numbers are hexagonal numbers, so it follows that even perfect numbers are always the sum of consecutive positive integers starting at 1, for example,
6 = sum_(n==1)^(3)n
(18)
28 = sum_(n==1)^(7)n
(19)
496 = sum_(n==1)^(31)n
(20)
(Singh 1997), where 3, 7, 31, ... (Sloane's A000668) are simply the Mersenne primes. In addition, every even perfect number P is of the form 2^(p-1)(2^p-1), so they can be generated using the identity
sum_(k==1)^(2^((p-1)/2))(2k-1)^3==2^(p-1)(2^p-1)==P.
(21)
It is known that all even perfect numbers (except 6) end in 16, 28, 36, 56, 76, or 96 (Lucas 1891) and have digital root 1. In particular, the last digits of the first few perfect numbers are 6, 8, 6, 8, 6, 6, 8, 8, 6, 6, 8, 8, 6, 8, 8, ... (Sloane's A094540), where the region between the 38th and 41st terms has been incompletely searched as of June 2004.
The sum of reciprocals of all the divisors of a perfect number is 2, since
n+...+c+b+a_()_(n)==2n
(22)
n/a+n/b+...==2n
(23)
1/a+1/b+...==2.
(24)
If s(n)>n, n is said to be an abundant number. If s(n)1, n is said to be a multiperfect number of order k.
The only even perfect number of the form x^3+1 is 28 (Makowski 1962).
Ruiz has shown that n is a perfect number iff
sum_(i==1)^(n-2)i|_n/i_|==1+sum_(i==1)^(n-1)i|_(n-1)/i_|.
Perfect numbers are positive integers n such that
n==s(n),
(1)
where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently
sigma(n)==2n,
(2)
where sigma(n) is the divisor function (i.e., the sum of divisors of n including n itself). For example, the first few perfect numbers are 6, 28, 496, 8128, ... (Sloane's A000396), since
6 = 1+2+3
(3)
28 = 1+2+4+7+14
(4)
496 = 1+2+4+8+16+31+62+124+248,
(5)
etc. The first few perfect numbers P_n are summarized in the following table together with their corresponding indices p (see below).
n p_n P_n
1 2 6
2 3 28
3 5 496
4 7 8128
5 13 33550336
6 17 8589869056
7 19 137438691328
8 31 2305843008139952128
Perfect numbers were deemed to have important numerological properties by the ancients, and were extensively studied by the Greeks, including Euclid.
Perfect numbers are also intimately connected with a class of numbers known as Mersenne primes, which are prime numbers of the form M_p==2^p-1. This can be demonstrated by considering a perfect number P of the form P==q.2^(p-1) where q is prime. By definition of a perfect number P,
sigma(P)==2P.
(6)
Now note that there are special forms for the divisor function sigma(n)
sigma(q)==q+1
(7)
for n==q a prime, and
sigma(2^alpha)==2^(alpha+1)-1
(8)
for n==2^alpha. Combining these with the additional identity
sigma(p_1^(alpha_1)p_2^(alpha_2)...p_r^(alpha_r))==sigma(p_1^(alpha_1))sigma(p_2^(alpha_2))...sigma(p_r^(alpha_r)),
(9)
where n==p_1^(alpha_1)p_2^(alpha_2)...p_r^(alpha_r) is the prime factorization of n, gives
sigma(P) = sigma(q.2^(p-1))
(10)
= sigma(q)sigma(2^(p-1))
(11)
= (q+1)(2^p-1).
(12)
But sigma(P)==2P, so
(q+1)(2^p-1)==2q.2^(p-1)==q.2^p.
(13)
Solving for q then gives
q==2^p-1.
(14)
Therefore, if P is to be a perfect number, q must be of the form q==2^p-1. Defining M_p as a prime number of the form M_P=q==2^p-1, it then follows that
P_p==1/2(M_p+1)M_p==2^(p-1)(2^p-1)
(15)
is a perfect number, as stated in Proposition IX.36 of Euclid's Elements (Dickson 1957, p. 3; Dunham 1990).
While many of Euclid's successors implicitly assumed that all perfect numbers were of the form (15) (Dickson 1952, pp. 3-33), the precise statement that all even perfect numbers are of this form was first considered in a 1638 letter from Descartes to Mersenne (Dickson 2005, p. 12). Proof or disproof that Euclid's construction gives all possible even perfect numbers was proposed to Fermat in a 1658 letter from Frans van Schooten (Dickson 2005, p. 14). In a posthumous paper, Euler (Euler 1849) provided the first proof that Euclid's construction gives all possible even perfect numbers (Dickson 2005, p. 19).
It is not known if any odd perfect numbers exist, although numbers up to 10^(300) have been checked (Brent et al. 1991; Guy 1994, p. 44) without success.
All even perfect numbers P>6 are of the form
P==1+9T_n,
(16)
where T_n is a triangular number
T_n==1/2n(n+1)
(17)
such that n==8j+2 (Eaton 1995, 1996). In addition, all even perfect numbers are hexagonal numbers, so it follows that even perfect numbers are always the sum of consecutive positive integers starting at 1, for example,
6 = sum_(n==1)^(3)n
(18)
28 = sum_(n==1)^(7)n
(19)
496 = sum_(n==1)^(31)n
(20)
(Singh 1997), where 3, 7, 31, ... (Sloane's A000668) are simply the Mersenne primes. In addition, every even perfect number P is of the form 2^(p-1)(2^p-1), so they can be generated using the identity
sum_(k==1)^(2^((p-1)/2))(2k-1)^3==2^(p-1)(2^p-1)==P.
(21)
It is known that all even perfect numbers (except 6) end in 16, 28, 36, 56, 76, or 96 (Lucas 1891) and have digital root 1. In particular, the last digits of the first few perfect numbers are 6, 8, 6, 8, 6, 6, 8, 8, 6, 6, 8, 8, 6, 8, 8, ... (Sloane's A094540), where the region between the 38th and 41st terms has been incompletely searched as of June 2004.
The sum of reciprocals of all the divisors of a perfect number is 2, since
n+...+c+b+a_()_(n)==2n
(22)
n/a+n/b+...==2n
(23)
1/a+1/b+...==2.
(24)
If s(n)>n, n is said to be an abundant number. If s(n)
The only even perfect number of the form x^3+1 is 28 (Makowski 1962).
Ruiz has shown that n is a perfect number iff
sum_(i==1)^(n-2)i|_n/i_|==1+sum_(i==1)^(n-1)i|_(n-1)/i_|.
Smith numbers
A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially satisfy this condition). One example of a Smith number is the beast number
666==2.3.3.37,
(1)
since
6+6+6==2+3+3+(3+7)==18.
(2)
Another Smith number is
4937775==3.5.5.65837,
(3)
since
4+9+3+7+7+7+5==3+5+5+(6+5+8+3+7)==42.
(4)
The first few Smith numbers are 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, ... (Sloane's A006753). The corresponding digits sums are 4, 4, 9, 13, 13, 13, 4, 13, 4, 13, 13, 13, 13, ... (Sloane's A050218). McDaniel (1987a) showed that there are an infinite number of Smith numbers.
A generalized k-Smith number can also be defined as a number m satisfying S_p(m)==kS(m), where S_p(m) is the sum of the digits of m's prime factors and S(m) is the usual sum of m's digits. The following table gives the first few k-Smith numbers for small integers and their inverses.
k Sloane k-Smith numbers
1/3 A050225 6969, 19998, 36399, 39693, 66099, 69663, ...
1/2 A050224 88, 169, 286, 484, 598, 682, 808, 844, 897, ...
1 A006753 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, ...
2 A104390 32, 42, 60, 70, 104, 152, 231, 315, 316, 322, ...
3 A104391 402, 510, 700, 1113, 1131, 1311, 2006, 2022, ...
A Smith number can be constructed from every factored repunit R_n (Hoffman 1998, pp. 205-206). The largest known Smith number is
9xR_(1031)(10^(4594)+3x10^(2297)+1)^(1476)x10^(3913210).
666==2.3.3.37,
(1)
since
6+6+6==2+3+3+(3+7)==18.
(2)
Another Smith number is
4937775==3.5.5.65837,
(3)
since
4+9+3+7+7+7+5==3+5+5+(6+5+8+3+7)==42.
(4)
The first few Smith numbers are 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, ... (Sloane's A006753). The corresponding digits sums are 4, 4, 9, 13, 13, 13, 4, 13, 4, 13, 13, 13, 13, ... (Sloane's A050218). McDaniel (1987a) showed that there are an infinite number of Smith numbers.
A generalized k-Smith number can also be defined as a number m satisfying S_p(m)==kS(m), where S_p(m) is the sum of the digits of m's prime factors and S(m) is the usual sum of m's digits. The following table gives the first few k-Smith numbers for small integers and their inverses.
k Sloane k-Smith numbers
1/3 A050225 6969, 19998, 36399, 39693, 66099, 69663, ...
1/2 A050224 88, 169, 286, 484, 598, 682, 808, 844, 897, ...
1 A006753 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, ...
2 A104390 32, 42, 60, 70, 104, 152, 231, 315, 316, 322, ...
3 A104391 402, 510, 700, 1113, 1131, 1311, 2006, 2022, ...
A Smith number can be constructed from every factored repunit R_n (Hoffman 1998, pp. 205-206). The largest known Smith number is
9xR_(1031)(10^(4594)+3x10^(2297)+1)^(1476)x10^(3913210).
Again the missing number
This trick is a bit more difficult then number 1 above, but once you discover 'the secret' and once you have practised this trick a few times (perhaps using pen and paper to begin with) you'll find it quite easy!
(a) Ask someone to write on a piece of paper (so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Ask them to add up all the digits of the number and tell you the result. Now, you don't need to remember this result, just continue adding the digits of the number that they tell you until you get a single digit 1 to 9 only. e.g. for 29, 2+9=11, 1+1=2, just remember 2! Call this number N.
(c) Then tell them (trying to seem like you are making these numbers up as you go) to add 6543 and write down the result. Then subtract 567 and write down this result. You can also continue and ask them to add or subtract other numbers like 432. Once you discover the 'secret' of this trick you'll see that many other numbers can be 'safely' added or subtracted and the trick still works!
(d) Now, as an option, you can let them choose which of the above results they wish to use. But whatever, ask them to add up the digits of the number and satisfy themselves that it is not the same as before!
(e) Ask them to circle any digit in the number selected except zero.
(f) They can then read out (slowly), all the other digits in random order. And you will tell them what the digit is that they circled.
(g) To find the missing digit, simply add up all the digits that they give you - repeatedly - until a single digit 1 to 9 is obtained. If this value is the same as the number N (see b. above), then the number they circled was 9. Otherwise, subtract this value from N. If this result is positive this is the number they circled! If negative, add 9 to the value and this is the number circled! e.g. If the digits are 9, 8, 8, and 4 then 9+8+8+4=29, 2+9=11, 1+1=2, If N=5, then 5-2=3 Therefore the number circled was 3. If N=1, then 1-2=-1, -1+9=8, the number circled was 8.
How does this trick work?
This trick works for the same reason that the first 'missing number trick' works - ‘digital roots’.
(a) Ask someone to write on a piece of paper (so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Ask them to add up all the digits of the number and tell you the result. Now, you don't need to remember this result, just continue adding the digits of the number that they tell you until you get a single digit 1 to 9 only. e.g. for 29, 2+9=11, 1+1=2, just remember 2! Call this number N.
(c) Then tell them (trying to seem like you are making these numbers up as you go) to add 6543 and write down the result. Then subtract 567 and write down this result. You can also continue and ask them to add or subtract other numbers like 432. Once you discover the 'secret' of this trick you'll see that many other numbers can be 'safely' added or subtracted and the trick still works!
(d) Now, as an option, you can let them choose which of the above results they wish to use. But whatever, ask them to add up the digits of the number and satisfy themselves that it is not the same as before!
(e) Ask them to circle any digit in the number selected except zero.
(f) They can then read out (slowly), all the other digits in random order. And you will tell them what the digit is that they circled.
(g) To find the missing digit, simply add up all the digits that they give you - repeatedly - until a single digit 1 to 9 is obtained. If this value is the same as the number N (see b. above), then the number they circled was 9. Otherwise, subtract this value from N. If this result is positive this is the number they circled! If negative, add 9 to the value and this is the number circled! e.g. If the digits are 9, 8, 8, and 4 then 9+8+8+4=29, 2+9=11, 1+1=2, If N=5, then 5-2=3 Therefore the number circled was 3. If N=1, then 1-2=-1, -1+9=8, the number circled was 8.
How does this trick work?
This trick works for the same reason that the first 'missing number trick' works - ‘digital roots’.
NO ELEPHANTS IN DENMARK TRICK.
This trick starts the same as the one above ... variations a, b and c can also be used!
(a) Ask someone to write on a piece of paper (secretly so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Tell them to rearrange the digits in that number and write it above the first number if it is larger but below it if smaller.
(c) Ask them to subtract the two numbers (they can use a calculator if they wish).
(d) Ask them to repeatedly add all the digits until they get a single digit 1 to 9. e.g. If the digits are 9, 8, 5, 4 and 3, then 9+8+5+4+3=29, 2+9=11, 1+1=2.
(e) Tell them to add 4 to this number and then add the two digits together again.
(f) Ask them to use this number to get a letter of the alphabet such that A=1, B=2 etc.
(g) Now, tell them to come up with the name of any country in the world that starts with this letter (get them to write it down).
(h) Then look at the second letter in the countries name and come up with an animal (or an Australian animal) that starts with this letter (get them to write it down).
(i) Then say, "the only trouble is that there are no elephants (or echidnas) in Denmark" and watch their faces drop with amazement at your psychic powers!
How does this trick work?
This trick works for the same reason that the one above works - ‘digital roots’. The country and animal part is just a bit of window dressing ... you will see immediately how this part of the trick works after you do it a couple of times!
(a) Ask someone to write on a piece of paper (secretly so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Tell them to rearrange the digits in that number and write it above the first number if it is larger but below it if smaller.
(c) Ask them to subtract the two numbers (they can use a calculator if they wish).
(d) Ask them to repeatedly add all the digits until they get a single digit 1 to 9. e.g. If the digits are 9, 8, 5, 4 and 3, then 9+8+5+4+3=29, 2+9=11, 1+1=2.
(e) Tell them to add 4 to this number and then add the two digits together again.
(f) Ask them to use this number to get a letter of the alphabet such that A=1, B=2 etc.
(g) Now, tell them to come up with the name of any country in the world that starts with this letter (get them to write it down).
(h) Then look at the second letter in the countries name and come up with an animal (or an Australian animal) that starts with this letter (get them to write it down).
(i) Then say, "the only trouble is that there are no elephants (or echidnas) in Denmark" and watch their faces drop with amazement at your psychic powers!
How does this trick work?
This trick works for the same reason that the one above works - ‘digital roots’. The country and animal part is just a bit of window dressing ... you will see immediately how this part of the trick works after you do it a couple of times!
Harder divisibility test
We can see by (a) above that most divisibility tests are now covered. The exception being prime numbers such as 7, 13, 17 ... So, here's the trick for divisibility by prime numbers (or multiples of). First find the first multiple of the number (let's call it N) that ends in 9 or 1 (e.g. 9, 11, 19, 21, 29...). Second, round up or down the number to the nearest multiple of ten (10, 20, 30...). Now your multiplying constant (let's call it K) becomes the tens digit (1, 2, 3...). If you rounded up it is positive (for add), if you rounded down it is negative (for subtract). Now take the number you wish to test for divisibility and multiply the units digit by K. This value is then added to the tens column or subtracted if K is negative. If the number that results is divisible by the number N then so is the original number! Of course, by logical extension, this process can be repeated until you recognize a number that is divisible by N.
Let's see if we can use this method to find a divisibility test for 7. First, multiply 7 until we have a number ending in 9 or 1. OK. 7, 14, 21. Now, we need to round this down to 20, so K = -2. Lets' test it. Try 3199. 319 - 2x9 = 301. 30 - 2 = 28. 28 is divisible by 7 so is 3199. Note, we could have gone further with 28. As 2-16 = -14. And 1-8 = -7. The factor K = -2 is also a test for divisibility by 21. The difference, being that we need to check if the result is divisible by 21 rather than 7! Let's try 9576. 957 - 2x6 = 945. 94 - 2x5 = 84. 8 - 2x4 = 0. The number 9576 is divisible by 21 (and 7 and 3 in fact). A couple of very interesting observations can be made. Firstly, all two digit numbers where the tens digit is twice the units digit (21, 42, 63 and 84) are all divisible by 21 (and by default 7 and 3). You should also notice the similarity of this test with the second test for divisibility by 3 above. In fact, this test can also be used to test for divisiblity by 3!
Alternatively, when testing for divisibility of 7, since 7x7 = 49, we can use K=+5. Let's try this with 294. 29 + 5x4 = 49. 49 is divisible by 7 and so is 294! Interestingly, we can't go any further with 49, since 4 + 5x9 = 49!
Note, despite what some books may tell you, tests for divisiblity by seven are not very 'practical'. I would recommend simply dividing the number by seven (you can discard the result if you're only interested in the remainder) and if the final remainder is zero then the number is divisible by seven! If you are using pen and paper then the number can be simplified first by crossing out 7's or any 2 digit multiple of 7 (make them 0), changing 8's to 1 and 9's to 2 (i.e. the remainders when divided by 7) and, since 7 divides into 1001, 10010, ... exactly, subtract one digit from another which are separated by 2 digits. Remember any leading or trailing zeros can be removed. e.g. Try 59633, cross off 63 = 59003, make 9 a 2 = 52003, subtract 3 from 2 = 49000, 49 is divisible by 7 so is 59633. Note, after obtaining 59003, the result could be obtained easier by taking the 3 from the 9 = 56000, 56 is divisible by 7! Also, since 1001 is a multiple of 7, K= -100. Which is the same as subtracting it from the 4th digit!
How about a divisibility test for 13? First 13, 26, 39. Round up to 40, therefore K = +4. Testing it, let's try 585. 58 + 4x5 = 78. 7 + 4x8 = 39. 39 is divisible by 13 and so is 585. What's real interesting about this method is that if testing for divisibility by 3 or 9, the value of K = +1. In other words, you repeatedly add the units digit to the tens column. If you continue to do this you end up with the digital root of the number! The value of K for other prime numbers is; K= -1 for 11. K= -5 for 17. K = +2 for 19. K= +7 for 23. Note, it's pretty easy to work out the values for K as required. i.e. There's no need to memorize them!
Finally, you may wish to find a negative value for K rather than use a positive value (the number reduces quicker and therefore the answer is found quicker). Simply subtract the number N from K. e.g. for N=3 and K=+1, the alternate value for K is 1-3 = -2. Try it and see if it works! To convert a negative K to a positive we can use N + K. e.g. for N=7 and K= -2, the alternate value of K is +5. For N=9, we can also use K= -8. For N=11, K= +10. etc. Note, with K= +10 for divisibility by 11, we can simply take the units digit and add it to the thousands column, if the resulting number is divisible by 11 so is the original number! Let's try 517, (5+7)1 = 121 we could stop here, but if we do it again (1+1)2 = 22. Clearly divisible by 11. Note, you can't go any further with this method (K= +10) once you have a 2 digit number. Of course, you could always continue with K= -1.
Let's see if we can use this method to find a divisibility test for 7. First, multiply 7 until we have a number ending in 9 or 1. OK. 7, 14, 21. Now, we need to round this down to 20, so K = -2. Lets' test it. Try 3199. 319 - 2x9 = 301. 30 - 2 = 28. 28 is divisible by 7 so is 3199. Note, we could have gone further with 28. As 2-16 = -14. And 1-8 = -7. The factor K = -2 is also a test for divisibility by 21. The difference, being that we need to check if the result is divisible by 21 rather than 7! Let's try 9576. 957 - 2x6 = 945. 94 - 2x5 = 84. 8 - 2x4 = 0. The number 9576 is divisible by 21 (and 7 and 3 in fact). A couple of very interesting observations can be made. Firstly, all two digit numbers where the tens digit is twice the units digit (21, 42, 63 and 84) are all divisible by 21 (and by default 7 and 3). You should also notice the similarity of this test with the second test for divisibility by 3 above. In fact, this test can also be used to test for divisiblity by 3!
Alternatively, when testing for divisibility of 7, since 7x7 = 49, we can use K=+5. Let's try this with 294. 29 + 5x4 = 49. 49 is divisible by 7 and so is 294! Interestingly, we can't go any further with 49, since 4 + 5x9 = 49!
Note, despite what some books may tell you, tests for divisiblity by seven are not very 'practical'. I would recommend simply dividing the number by seven (you can discard the result if you're only interested in the remainder) and if the final remainder is zero then the number is divisible by seven! If you are using pen and paper then the number can be simplified first by crossing out 7's or any 2 digit multiple of 7 (make them 0), changing 8's to 1 and 9's to 2 (i.e. the remainders when divided by 7) and, since 7 divides into 1001, 10010, ... exactly, subtract one digit from another which are separated by 2 digits. Remember any leading or trailing zeros can be removed. e.g. Try 59633, cross off 63 = 59003, make 9 a 2 = 52003, subtract 3 from 2 = 49000, 49 is divisible by 7 so is 59633. Note, after obtaining 59003, the result could be obtained easier by taking the 3 from the 9 = 56000, 56 is divisible by 7! Also, since 1001 is a multiple of 7, K= -100. Which is the same as subtracting it from the 4th digit!
How about a divisibility test for 13? First 13, 26, 39. Round up to 40, therefore K = +4. Testing it, let's try 585. 58 + 4x5 = 78. 7 + 4x8 = 39. 39 is divisible by 13 and so is 585. What's real interesting about this method is that if testing for divisibility by 3 or 9, the value of K = +1. In other words, you repeatedly add the units digit to the tens column. If you continue to do this you end up with the digital root of the number! The value of K for other prime numbers is; K= -1 for 11. K= -5 for 17. K = +2 for 19. K= +7 for 23. Note, it's pretty easy to work out the values for K as required. i.e. There's no need to memorize them!
Finally, you may wish to find a negative value for K rather than use a positive value (the number reduces quicker and therefore the answer is found quicker). Simply subtract the number N from K. e.g. for N=3 and K=+1, the alternate value for K is 1-3 = -2. Try it and see if it works! To convert a negative K to a positive we can use N + K. e.g. for N=7 and K= -2, the alternate value of K is +5. For N=9, we can also use K= -8. For N=11, K= +10. etc. Note, with K= +10 for divisibility by 11, we can simply take the units digit and add it to the thousands column, if the resulting number is divisible by 11 so is the original number! Let's try 517, (5+7)1 = 121 we could stop here, but if we do it again (1+1)2 = 22. Clearly divisible by 11. Note, you can't go any further with this method (K= +10) once you have a 2 digit number. Of course, you could always continue with K= -1.
Harder divisibility test
We can see by (a) above that most divisibility tests are now covered. The exception being prime numbers such as 7, 13, 17 ... So, here's the trick for divisibility by prime numbers (or multiples of). First find the first multiple of the number (let's call it N) that ends in 9 or 1 (e.g. 9, 11, 19, 21, 29...). Second, round up or down the number to the nearest multiple of ten (10, 20, 30...). Now your multiplying constant (let's call it K) becomes the tens digit (1, 2, 3...). If you rounded up it is positive (for add), if you rounded down it is negative (for subtract). Now take the number you wish to test for divisibility and multiply the units digit by K. This value is then added to the tens column or subtracted if K is negative. If the number that results is divisible by the number N then so is the original number! Of course, by logical extension, this process can be repeated until you recognize a number that is divisible by N.
Let's see if we can use this method to find a divisibility test for 7. First, multiply 7 until we have a number ending in 9 or 1. OK. 7, 14, 21. Now, we need to round this down to 20, so K = -2. Lets' test it. Try 3199. 319 - 2x9 = 301. 30 - 2 = 28. 28 is divisible by 7 so is 3199. Note, we could have gone further with 28. As 2-16 = -14. And 1-8 = -7. The factor K = -2 is also a test for divisibility by 21. The difference, being that we need to check if the result is divisible by 21 rather than 7! Let's try 9576. 957 - 2x6 = 945. 94 - 2x5 = 84. 8 - 2x4 = 0. The number 9576 is divisible by 21 (and 7 and 3 in fact). A couple of very interesting observations can be made. Firstly, all two digit numbers where the tens digit is twice the units digit (21, 42, 63 and 84) are all divisible by 21 (and by default 7 and 3). You should also notice the similarity of this test with the second test for divisibility by 3 above. In fact, this test can also be used to test for divisiblity by 3!
Alternatively, when testing for divisibility of 7, since 7x7 = 49, we can use K=+5. Let's try this with 294. 29 + 5x4 = 49. 49 is divisible by 7 and so is 294! Interestingly, we can't go any further with 49, since 4 + 5x9 = 49!
Note, despite what some books may tell you, tests for divisiblity by seven are not very 'practical'. I would recommend simply dividing the number by seven (you can discard the result if you're only interested in the remainder) and if the final remainder is zero then the number is divisible by seven! If you are using pen and paper then the number can be simplified first by crossing out 7's or any 2 digit multiple of 7 (make them 0), changing 8's to 1 and 9's to 2 (i.e. the remainders when divided by 7) and, since 7 divides into 1001, 10010, ... exactly, subtract one digit from another which are separated by 2 digits. Remember any leading or trailing zeros can be removed. e.g. Try 59633, cross off 63 = 59003, make 9 a 2 = 52003, subtract 3 from 2 = 49000, 49 is divisible by 7 so is 59633. Note, after obtaining 59003, the result could be obtained easier by taking the 3 from the 9 = 56000, 56 is divisible by 7! Also, since 1001 is a multiple of 7, K= -100. Which is the same as subtracting it from the 4th digit!
How about a divisibility test for 13? First 13, 26, 39. Round up to 40, therefore K = +4. Testing it, let's try 585. 58 + 4x5 = 78. 7 + 4x8 = 39. 39 is divisible by 13 and so is 585. What's real interesting about this method is that if testing for divisibility by 3 or 9, the value of K = +1. In other words, you repeatedly add the units digit to the tens column. If you continue to do this you end up with the digital root of the number! The value of K for other prime numbers is; K= -1 for 11. K= -5 for 17. K = +2 for 19. K= +7 for 23. Note, it's pretty easy to work out the values for K as required. i.e. There's no need to memorize them!
Finally, you may wish to find a negative value for K rather than use a positive value (the number reduces quicker and therefore the answer is found quicker). Simply subtract the number N from K. e.g. for N=3 and K=+1, the alternate value for K is 1-3 = -2. Try it and see if it works! To convert a negative K to a positive we can use N + K. e.g. for N=7 and K= -2, the alternate value of K is +5. For N=9, we can also use K= -8. For N=11, K= +10. etc. Note, with K= +10 for divisibility by 11, we can simply take the units digit and add it to the thousands column, if the resulting number is divisible by 11 so is the original number! Let's try 517, (5+7)1 = 121 we could stop here, but if we do it again (1+1)2 = 22. Clearly divisible by 11. Note, you can't go any further with this method (K= +10) once you have a 2 digit number. Of course, you could always continue with K= -1.
Let's see if we can use this method to find a divisibility test for 7. First, multiply 7 until we have a number ending in 9 or 1. OK. 7, 14, 21. Now, we need to round this down to 20, so K = -2. Lets' test it. Try 3199. 319 - 2x9 = 301. 30 - 2 = 28. 28 is divisible by 7 so is 3199. Note, we could have gone further with 28. As 2-16 = -14. And 1-8 = -7. The factor K = -2 is also a test for divisibility by 21. The difference, being that we need to check if the result is divisible by 21 rather than 7! Let's try 9576. 957 - 2x6 = 945. 94 - 2x5 = 84. 8 - 2x4 = 0. The number 9576 is divisible by 21 (and 7 and 3 in fact). A couple of very interesting observations can be made. Firstly, all two digit numbers where the tens digit is twice the units digit (21, 42, 63 and 84) are all divisible by 21 (and by default 7 and 3). You should also notice the similarity of this test with the second test for divisibility by 3 above. In fact, this test can also be used to test for divisiblity by 3!
Alternatively, when testing for divisibility of 7, since 7x7 = 49, we can use K=+5. Let's try this with 294. 29 + 5x4 = 49. 49 is divisible by 7 and so is 294! Interestingly, we can't go any further with 49, since 4 + 5x9 = 49!
Note, despite what some books may tell you, tests for divisiblity by seven are not very 'practical'. I would recommend simply dividing the number by seven (you can discard the result if you're only interested in the remainder) and if the final remainder is zero then the number is divisible by seven! If you are using pen and paper then the number can be simplified first by crossing out 7's or any 2 digit multiple of 7 (make them 0), changing 8's to 1 and 9's to 2 (i.e. the remainders when divided by 7) and, since 7 divides into 1001, 10010, ... exactly, subtract one digit from another which are separated by 2 digits. Remember any leading or trailing zeros can be removed. e.g. Try 59633, cross off 63 = 59003, make 9 a 2 = 52003, subtract 3 from 2 = 49000, 49 is divisible by 7 so is 59633. Note, after obtaining 59003, the result could be obtained easier by taking the 3 from the 9 = 56000, 56 is divisible by 7! Also, since 1001 is a multiple of 7, K= -100. Which is the same as subtracting it from the 4th digit!
How about a divisibility test for 13? First 13, 26, 39. Round up to 40, therefore K = +4. Testing it, let's try 585. 58 + 4x5 = 78. 7 + 4x8 = 39. 39 is divisible by 13 and so is 585. What's real interesting about this method is that if testing for divisibility by 3 or 9, the value of K = +1. In other words, you repeatedly add the units digit to the tens column. If you continue to do this you end up with the digital root of the number! The value of K for other prime numbers is; K= -1 for 11. K= -5 for 17. K = +2 for 19. K= +7 for 23. Note, it's pretty easy to work out the values for K as required. i.e. There's no need to memorize them!
Finally, you may wish to find a negative value for K rather than use a positive value (the number reduces quicker and therefore the answer is found quicker). Simply subtract the number N from K. e.g. for N=3 and K=+1, the alternate value for K is 1-3 = -2. Try it and see if it works! To convert a negative K to a positive we can use N + K. e.g. for N=7 and K= -2, the alternate value of K is +5. For N=9, we can also use K= -8. For N=11, K= +10. etc. Note, with K= +10 for divisibility by 11, we can simply take the units digit and add it to the thousands column, if the resulting number is divisible by 11 so is the original number! Let's try 517, (5+7)1 = 121 we could stop here, but if we do it again (1+1)2 = 22. Clearly divisible by 11. Note, you can't go any further with this method (K= +10) once you have a 2 digit number. Of course, you could always continue with K= -1.
Multiplying numbers between 11 and 19
Multiplying numbers between 11 and 19............
Now, to do this in your head, we are going to use a similar technique to that in (a) above. As long as you know your times tables and can add some simple sums you'll be able to do this - with practice! First let's try 12x13. 12-10=2 and 13-10=3 (i.e. just take the units digits). Either add 13+2 or 12+3 = 15 (this is the tens digit = 150). Multiply 2x3 = 6 (this is the units). Add 150+6 = 156 is the answer. Let's try 17x18. Add 17+8 or 18+7 = 25. Multiply 8x7 = 56. Add 250+56 = 306 is the answer. How about squaring numbers between 13 and 19...easy! Let's do 16 squared. 16+6=22, 6x6=36, then 220+36 = 256 is the answer!
P.S. Once you have mastered doing this in you head, you will then be able to multiply any numbers between 0 and 20 in your head. But what about single digit (2..9) multiplied by double digit numbers? Easy. You can simply use long multiplication! Here's how. Try 8x19 = 8x9 + 80 = 152. Try 6x14 = 6x4 + 60 = 84.
Now, to do this in your head, we are going to use a similar technique to that in (a) above. As long as you know your times tables and can add some simple sums you'll be able to do this - with practice! First let's try 12x13. 12-10=2 and 13-10=3 (i.e. just take the units digits). Either add 13+2 or 12+3 = 15 (this is the tens digit = 150). Multiply 2x3 = 6 (this is the units). Add 150+6 = 156 is the answer. Let's try 17x18. Add 17+8 or 18+7 = 25. Multiply 8x7 = 56. Add 250+56 = 306 is the answer. How about squaring numbers between 13 and 19...easy! Let's do 16 squared. 16+6=22, 6x6=36, then 220+36 = 256 is the answer!
P.S. Once you have mastered doing this in you head, you will then be able to multiply any numbers between 0 and 20 in your head. But what about single digit (2..9) multiplied by double digit numbers? Easy. You can simply use long multiplication! Here's how. Try 8x19 = 8x9 + 80 = 152. Try 6x14 = 6x4 + 60 = 84.
THE MISSING NUMBER TRICK.
(a) Ask someone to write on a piece of paper (so you can’t see it) a large number (I suggest 5 digits to start with).
(b) Ask them to rearrange the digits in that number and write it above the first number if it is larger but below it if smaller.
(c) Then tell them to subtract the two numbers (they can use a calculator if they wish).
(d) Ask them to circle any digit in the result except zero.
(e) They can then read out (slowly), all the other digits in random order. And you will tell them what the digit is that they circled.
(f) To find the missing digit, simply add up all the digits that they give you - repeatedly - until a single digit 1 to 9 is obtained. If this value is 9, then the number they circled was 9. Otherwise, add a value to the number until it is 9. This value is the number they circled! e.g. If the digits are 9, 8, 8 and 4, then 9+8+8+4=29, 2+9=11, 1+1=2. 9-2=7. Therefore the number circled was 7.
(b) Ask them to rearrange the digits in that number and write it above the first number if it is larger but below it if smaller.
(c) Then tell them to subtract the two numbers (they can use a calculator if they wish).
(d) Ask them to circle any digit in the result except zero.
(e) They can then read out (slowly), all the other digits in random order. And you will tell them what the digit is that they circled.
(f) To find the missing digit, simply add up all the digits that they give you - repeatedly - until a single digit 1 to 9 is obtained. If this value is 9, then the number they circled was 9. Otherwise, add a value to the number until it is 9. This value is the number they circled! e.g. If the digits are 9, 8, 8 and 4, then 9+8+8+4=29, 2+9=11, 1+1=2. 9-2=7. Therefore the number circled was 7.
squaring shortcut for 5 ending number
Here is a really quick way to square any number with a 5 on the end.
Lets take
Ok, so what you have to do is split up the numbers, giving you
and
Forget about the for the moment and do this:
Always add 1, adding 1 to the 4, so we get 4 + 1 = 5
Then multiply this answer, 5, by the original first number, 4
5 X 4 = 20
So what you have is 20 and
Everyone knows = 25 right? Well it does. This is what makes it easy.
Put the two answers together and that's the answer!
2025
This works for any number ending in but when the numbers get over 100 it tends to get a little trickier with the multiplication.
Give it a try with another number.
Try , it isn't difficult.
Split the numbers apart:
8 and
Again, forget about the
Add 1 to 8
8 + 1 = 9
Multiply 9 by the first number, which was 8
9 X 8 =72
Now, put all the numbers together, 72 and
= 25
So the answer is 7225
Try it out in a calculator once you have done it.
Lets take
Ok, so what you have to do is split up the numbers, giving you
and
Forget about the for the moment and do this:
Always add 1, adding 1 to the 4, so we get 4 + 1 = 5
Then multiply this answer, 5, by the original first number, 4
5 X 4 = 20
So what you have is 20 and
Everyone knows = 25 right? Well it does. This is what makes it easy.
Put the two answers together and that's the answer!
2025
This works for any number ending in but when the numbers get over 100 it tends to get a little trickier with the multiplication.
Give it a try with another number.
Try , it isn't difficult.
Split the numbers apart:
8 and
Again, forget about the
Add 1 to 8
8 + 1 = 9
Multiply 9 by the first number, which was 8
9 X 8 =72
Now, put all the numbers together, 72 and
= 25
So the answer is 7225
Try it out in a calculator once you have done it.
Adding Time
Adding Time
Here is a nice simple way to add hours and minutes together:
Let's add 1 hr and 35 mins and 3 hr 55 mins together.
What you do is this:
make the 1 hr 35 mins into one number, which will give us 135 and do the same for the other number giving us 355
Now you want to add these two numbers together:
135
355
____
490
So we now have a sub total of 490. What you need to do to this and all sub totals is add the time constant of 40.
No matter what the hours and mins are, just add the 40 time constant to the sub total.
490 + 40 = 530
So we can now see our answer is 5 hrs and 30 mins!
Here is a nice simple way to add hours and minutes together:
Let's add 1 hr and 35 mins and 3 hr 55 mins together.
What you do is this:
make the 1 hr 35 mins into one number, which will give us 135 and do the same for the other number giving us 355
Now you want to add these two numbers together:
135
355
____
490
So we now have a sub total of 490. What you need to do to this and all sub totals is add the time constant of 40.
No matter what the hours and mins are, just add the 40 time constant to the sub total.
490 + 40 = 530
So we can now see our answer is 5 hrs and 30 mins!
Thursday, August 02, 2007
Why is it always 1089
You will need a little bit off algebra.
But stick with it, it is not difficult.
Represent the number with ABC
Reverse this to get CBA
Remember that A is Hundreds B is tens and C is units
Take CBA from ABC like this
Hundreds Tens Units
A B C
C B A
Now here is the trick: subtract 1 Hundred, and add 9 Tens and 10 Ones (-100, +90, +10 = 0, so won't change answer):
Hundreds Tens Units
A-1A B+9B 10+CC
C B A
A-1-C 9 10+C-A
Last Step: Reverse the answer and add the two numbers together.
A-1-C 9 10+C-A
+
10+C-A 9 A-1-C
9 18 9
(simplify:)
10 8 9
As predicted the answer was 1089
Note:But sometimes I ended with 198 not 1089. This happens if you pick a number like 546. Try to pick consecutive numbers like 123, 345, 765 etc. If it does happen, it is not a problem. Just repeat the stages again starting from 198.
But stick with it, it is not difficult.
Represent the number with ABC
Reverse this to get CBA
Remember that A is Hundreds B is tens and C is units
Take CBA from ABC like this
Hundreds Tens Units
A B C
C B A
Now here is the trick: subtract 1 Hundred, and add 9 Tens and 10 Ones (-100, +90, +10 = 0, so won't change answer):
Hundreds Tens Units
A-1A B+9B 10+CC
C B A
A-1-C 9 10+C-A
Last Step: Reverse the answer and add the two numbers together.
A-1-C 9 10+C-A
+
10+C-A 9 A-1-C
9 18 9
(simplify:)
10 8 9
As predicted the answer was 1089
Note:But sometimes I ended with 198 not 1089. This happens if you pick a number like 546. Try to pick consecutive numbers like 123, 345, 765 etc. If it does happen, it is not a problem. Just repeat the stages again starting from 198.
1089
Always End With 1089
Add two number together and always end with 1089.
Here is How:
Pick a three digit number. The three numbers used must be different. i.e. 123 Reverse that number. 123 becomes 321
Take the smallest three digit number from the largest.
321 - 123 = 198
Take the answer and reverse that number. 198 becomes 891
Add that number to the answer of the subtraction. 891 + 198 = 1089
The answer will be 1089!
Add two number together and always end with 1089.
Here is How:
Pick a three digit number. The three numbers used must be different. i.e. 123 Reverse that number. 123 becomes 321
Take the smallest three digit number from the largest.
321 - 123 = 198
Take the answer and reverse that number. 198 becomes 891
Add that number to the answer of the subtraction. 891 + 198 = 1089
The answer will be 1089!
