Some online resources on geometry that computer scientists might enjoy reading in their spare time:
1) Geometry Unbound by Kiran Kedlaya. This book provides a solid grounding in geometry for IMO competitions.
2) Introduction to the Geometry of the Triangle and A Tour of Triangle Geometry (pdf) by Paul Yiu are very interesting. Four triangle centers have been known since antiquity: centroid, orthocenter, incenter and circumcenter. Later, between 1700 and 1900, roughly ten more ‘triangle centers’ were discovered. Since 1980s, with the help of computers, many more triangle centers have been discovered. Clark Kimberling has been maintaining the Encyclopedia of Triangle Centers, which now lists 3000+ triangle centers!
3) Paul Yiu has also written a 360-page Recreational Mathematics (pdf) with plenty of geometric theorems and puzzles. Paul Yiu has also authored Elegant Geometric Constructions.
4) Geometry at Cut-The-Knot by Alex Bogomolny.
5) Sangaku (Japanese Temple Geometry): Diagrams with lines, circles, ellipses and arcs that suggest a theorem — without proof! Many of these problems are quite challenging — Sangaku problems at cut-the-knot.org and Sangaku Sketchpad files. A recent book: Sacred Mathematics: Japanese Temple Geometry (392 pages, 2008) by Fukagawa Hidetoshi and Tony Rothman.
