Category Archives: iteration

Recounting the Rationals, part IVb: the Euclidean Algorithm

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

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

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

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