Pictures and Proofs

On the basis of the paper you should have develop a definitive essay on the pros and cons of using pictures to support mathematical proofs. Is "a picture worth a thousan words?" Or is a picture an illusion that given incomplete and often erroneous understanding. Please examine this problem from your viewpoint at a teacher of mathematics and from your viewpoint as a student of mathematics. Commnent on the nature of the pictures and the importance of accuracy. Length: 500 - 1000 words.

There are ample Web resources: Here are just a few.

1. An entire threaded discussion on this subject can be found at http://forum.swarthmore.edu/epigone/historia_matematica/blarwhufror
   
2. I have begun to develop a geometry Website using the concept of stepped illustrations and proofs. You can find it at http://www.academicsolutions.com/mathtools/javageo/index.htm
3. Proofs Without Words by Roger B. Nelsen is an entire book dedicated to showing how to prove mathematical results using pictures as visual clues. From promotional material we have: Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. It can be found at http://www.maa.org/pubs/books/pww.html
4. Pictures and Mathematics by Tamara Munzner. See, http://www.geom.umn.edu/docs/research/ieee94/node2.html
5. Thirty two proofs of the Pythagorean theorem. Here is that theorem with the foremost visual interpretation. Indeed, in many cases the picture is the proof. http://www.cut-the-knot.com/pythagoras/

As an alternative to this essay you can prepare a comprehensive list of resources on this subject and their Web addresses.