Friday, May 18, 2012

Compass and Straightedge geometry meets HTML5

This is a proof of concept build of an HTML5 engine to perform classical Greek compass and straightedge calculations, as described in this Wikipedia article. In brief, an initial set of points can be created, and then points can be connected by lines, circles can be drawn with one point as center and another as one point in the circumference, and finally the points where circles and/or lines intersect can be added as new points. With those simple rules, angles and line segments can be bisected, and certain regular (equilateral) shapes can be created.

I have created a rudimentary language to describe the adding of points, lines, and circles, and finding their intersections, which I discuss briefly after the demo below. Without further ado, choose a sample "program" to run to bisect an angle or create a regular shape. If you're a fan of Gauss, be sure to check out the heptadecagon.

Thursday, May 10, 2012

Animated prime number machine

This uses the HTML5 canvas architecture, so no IE8 or less; sorry. I have only tested it with Google Chrome, so it may not work in other HTML5-capable browsers. If you find this to be the case, please leave feedback with any errors you see, and what browser version you're using, and I'll see what I can do to get it working for you.

The principle of the prime number machine is of rolling coins and elevators. I created this because I thought it would be neat to have a way for prime numbers to be produced by a set of mechanical rules rather than with pure mathematical methods. Here is a basic description of the rules:

  • If a coin rolls into an empty box, it creates an elevator with the height shown on the coin, and a new empty box appears.
  • If a coin hits the top or bottom of an existing elevator, it bounces off with no effect.
  • The coin's number increments after each cycle
  • The elevators go down a floor during each cycle until the top car is flush with the ground line, then they begin going back up to where they started.

This results in two basic phenomena: All new elevators correspond to prime numbers. When a coin does not have a prime number on it, all of the elevators corresponding to the coin's prime factors have a car flush with the ground.