Department of Mathematics

It may well be doubted whether, in all the range of science, there is any field so fascinating to the explorer -- so rich with hidden treasures -- so fruitful in delightful surprises -- as Pure Mathematics.

Lewis Carroll, quoted in The Heart of Mathematics by E. Burger and M. Starbird.

• Escher's World. This site is a "visual" mathematics site. It contains (among other things) an applet that allows you to explore different tesselations of the plane in a dynamic way.
  
• Escher's "Ascending and Descending in Lego" Andrew Lipson has recreated Escher's Ascending Descending" painting (which is an optical illusion) using Lego's. The picture was not doctored in any way to achieve the optical illusion; however, the picture was taken at just the right angle. . Mr. Lipson includes a description, and pictures of how this was accomplished.
  
• Exploring the Shape of Space Jeff weeks has created a wonderful site to explore the geometry and topology of 2- and 3-dimensional space. This site also includes games such as tic-tac-toe, chess, word search, crosswords, mazes, and jigsaw puzzles on the torus and the klein bottle.
  
• Stereoscopic Animated Hypercube. This site allows you to "see" a four dimensional cube. To really get the full effect of this sight you need to use 3D glasses.
  
• The Geometry Center. Although the Geometry Center is now closed, its web site remains and is a repository for projects that were under taken by the Geometry Center which specialized in the use of technology to visualize and communicate mathematics and related sciences.
  
• Thomas Banchoff's Project LIst. This site gives a list of projects that Thomas Banchoff is working on. Most of these involve computer visualization of mathematical concepts.
  
• The Dynamical Systems and Technology Project at Boston University. This site is designed to help secondary and college teachers bring topics like chaos an fractals into the classroom. It contains applets to play games using chaos or fractals, create fractal movies on your computer, and generally explore the mathematics behind chaos and fractals.
  
• Java Julia Set Generator. This site allows you to see the Julia Set for any point inside the Mandelbrot Set.
  
• The Scientific Graphics Project. This site contains information and pictures of minimal surfaces.
  
• Proof. Proof is a play by David Auburn about a once-brilliant but now aging mathematician who suffers from manic depression and is cared for by his brilliant, 25-year old daughter who is torn between following as her father's protege and meeting his same mental fate. The play includes wonderful, enriching mathematical history and stories, but does not require any mathematical prerequisets. It started running on Broadway in 2000 to critical acclaim. Proof is also a 2005 film starring Anthony Hopkins, Gwyneth Paltrow, Jake Gyllenhaal, and Hope Davis. It is now also available on DVD.
• Revisiting Flatland: Navigating Between the Dimensions, Julian Fleron, Volker Ecke, to appear in "Geometry Focus Edition" of the "Mathematics Teacher" (National Council of Teachers of Mathematics), 2011.
• Mathematics and Salsa Dancing, Christine von Renesse, Volker Ecke, Journal of Mathematics and the Arts, March 2011, Vol. 5, No. 1.