BMAD's chaos puzzle gave an algorithm for recursively placing points,
ad infinitum, within the interior of a triangle. The beautifully surprising
result was the appearance of well-defined areas, within which points
could not be placed. Call these areas white space.
them, of several other shapes. The most interesting seemed to be
BMAD's original triangle, and the trapezoid, reproduced below.
My puzzle is a simple calculation:
What fraction of the triangle is white space?
What fraction of the trapezoid is white space?
Edit: Creativity will be rewarded: Got a different approach? Get another star.
Edited by bonanova, 29 July 2013 - 03:37 AM.