Examples of Visualizations and "Snapshots" Sum of integers from 1 to n--Example of proof with pictures. The Klein bottle--A virtual image, with animation. Circumcircle of a Triangle--Drawn with GeoGebra. Try downloading GeoGebra and doing this yourself. Non-Euclid--Hyperbolic geometry sketchpad. Try constructing the circumcircle of a triangle. The Kiss Precise--A theorem of mathematics expressed in the form of a poem. Crucifixion Hypercubus--A hypercube (4-cube) in the art of Salvadore Dali. Kenneth Snelson--Artist who has done significant work with tensegrity. Platonic Solids--Virtual image. POV-Ray Hall of Fame--Images produced by ray-tracing software. Brass and Steel--Movie produced by ray-tracing software. Animusic--Animations of fictional musical instruments. Consecutive Number Puzzle---Reasoning about reasoning. Square Dance---Illustrating symmetries with movement. Four-Dimensional Tic-Tac-Toe---Visualizing the hypercube. The Pythagorean Theorem---Another proof with pictures. Extra-Terrestrial Communication---Exploiting the idea that mathematics is universal.