Category Archives: iteration

Recounting the Rationals, part IVb: the Euclidean Algorithm

Posted on February 11, 2008 by Brent

Suppose we have two integers, and we’d like to find their greatest common divisor (GCD). Recall that the greatest common divisor of two integers m and n is exactly that: the greatest integer which is a divisor of both m … Continue reading →

Posted in computation, iteration, number theory | 15 Comments

The Fibonacci sequence: an introduction

Posted on July 22, 2007 by Brent

The Fibonacci sequence is probably one of the most famous — and most widely written-about — number sequences in all of mathematics. So why write about it, if it’s been written about so much already? Well, because I can, and … Continue reading →

Posted in famous numbers, fibonacci, iteration, pattern, sequences | 11 Comments

Open problems: Collatz conjecture

Posted on May 8, 2007 by Brent

Pick any integer you like. Got an integer? OK, now apply this simple rule: if the integer is even, divide by two; otherwise, multiply by three and add one. For example, if you started with 10, you would get 5; … Continue reading →

Posted in iteration, open problems, sequences | 33 Comments

The Mandelbrot Set

Posted on May 8, 2006 by Brent

For those of you already familiar with the Mandelbrot Set, I suppose this will be like visiting with an old friend. For those of you who aren’t — you’re in for a treat! Okay, you say, that looks pretty cool … Continue reading →

Posted in convergence, fractals, infinity, iteration | 1 Comment