Links to lovely collections of math art, fractal images, computational geometry, mathematical visualizations, etc. A collection of graphics illustrating the 17 plane symmetry groups with wallpaper patterns, by David Joyce at Clark University. Xah Lee's Tilings and Patterns site contains a large collection of wallpaper designs based on geometrical motifs, Mathematica software, and links to many other related sites. Mark Phillips' Java Kali lets you draw wallpaper patterns based on any of the 17 plane symmetry groups. The images were created with KnotPlot, a program to visualize and manipulate mathematical knots in three and four dimensions.
Proofs are usually dry, dusty stuff sprinkled liberally with symbols.
This proof of the Pythagorean Theorem is attributed to Bhaskara, a Hindu mathematician of the 12th century. We are given the bottom right triangle. Construct a square by making three copies of the triangle, as shown. The area of all four triangles is 2ab.