Monthly Archives: November 2007

Google open-source programming contest

Posted on November 28, 2007 by Brent

Are you a high school student? Are you interested in computer programming? You should participate in the Google Highly Open Participation Contest! The idea is that students compete to contribute features to various open source projects. You’re guaranteed to get … Continue reading →

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Perfect numbers, part III

Posted on November 27, 2007 by Brent

This is the last in a series of posts about perfect numbers. A quick recap of the series so far: in part I, I defined perfect numbers as positive integers n for which , where denotes the sum of the … Continue reading →

Posted in algebra, number theory, open problems, primes, solutions | 11 Comments

Video: The Story of Pi

Posted on November 26, 2007 by Brent

A fun video about , including a nice visual explanation of the formula for the area of a circle, and some interesting places that shows up where you might not expect it to. The video was made by Tom M. … Continue reading →

Posted in famous numbers, geometry, links, video | 5 Comments

Perfect numbers, interlude (Challenge #11)

Posted on November 20, 2007 by Brent

Recall that the first three perfect numbers are 6, 28, and 496. And if you tried computing as I suggested near the end of part I, you might have noticed that 8128 is perfect as well! Do you see any … Continue reading →

Posted in challenges, famous numbers, number theory | 4 Comments

Video: Möbius transformations revealed

Posted on November 18, 2007 by Brent

For your viewing pleasure, a fantastically beautiful video about Möbius transformations, which are functions of the form where z, a, b, c, and d are complex numbers, and . For example, is a Möbius transformation with b=2, c=1, and a=d=0. … Continue reading →

Posted in complex numbers, geometry, video | Comments Off

Perfect numbers, part II

Posted on November 15, 2007 by Brent

In my last post I introduced the concept of perfect numbers, which are positive integers n for which , where denotes the sum of all the divisors of n. Incidentally, we could write the definition of as , that is, … Continue reading →

Posted in algebra, famous numbers, number theory | 8 Comments

Perfect numbers, part I

Posted on November 12, 2007 by Brent

Today I’d like to talk about perfect numbers, which touch on some clever algebra and some neat topics in number theory. At least, I’ll start talking about them, since it will probably take me three or four posts to say … Continue reading →

Posted in famous numbers, number theory, sequences | 3 Comments

Menger sponge video

Posted on November 10, 2007 by Brent

Check out the following totally sweet video of zooming into a Menger sponge! This video was made by David Makin, who has lots of other cool images and videos at his website. You can probably figure out what a Menger … Continue reading →

Posted in fractals, video | 6 Comments

Geometric multiplication: an explanation

Posted on November 10, 2007 by Brent

Now for an explanation/proof of that weird method of multiplication that I talked about in a previous post. You’ll recall that it’s really quite simple: to multiply a and b, draw a line from to and see where it crosses … Continue reading →

Posted in algebra, geometry, proof | Comments Off

Geometric multiplication

Posted on November 8, 2007 by Brent

I’ve just learned about a fairly useless, yet utterly beguiling method for performing multiplication, and I’d like to share it! Suppose you have two numbers you wish to multiply, call them a and b. Your first instinct is probably to … Continue reading →

Posted in algebra, geometry, links, people | 4 Comments