# Monthly Archives: November 2007

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

## Perfect numbers, part III

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

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

## Perfect numbers, interlude (Challenge #11)

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

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 on Video: Möbius transformations revealed

## Perfect numbers, part II

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

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

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

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 on Geometric multiplication: an explanation

## Geometric multiplication

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