When I have some time (when I retire?) I would like to collect in this page the most interesting incorrect proofs and algorithms in the field of geometry. Like psychologists with illusions, I am fascinated by those things that don't work as we expect them to, and why they don't. In the mean time, below are some interesting references.

Proofs:

• Scientific Practice and Thinking - A Course
• Proof - The International Newsletter on Teaching and Learning Mathematical Proof
• PLUS - A great math thinking site
• L. I. Golovina and I. M. Yaglom, Induction in Geometry, Mir Publishers, Moscow, 1979. [Examples of how to prove geometry theorems using induction.]
• A. I. Fetisov, Proof in Geometry, Mir Publishers, Moscow, 1978. [A nice elementary discussion on what is a proof, when and why it is necessary and what things may be accepted without proof.]
• I. Kleiner and N. Movshovitz-Hadar, "Proof: A Many-Splendored Thing," The Mathematical Intelligencer, vol. 19, No. 3, Summer 1997, pp. 16-26. [A fascinating historical perspective on proving things.]
• Selected publications on Proof

Refutations:

• Bryan Bunch, Mathematical Fallacies and Paradoxes, Dover publications, Inc., Mineola, New York, 1982.
• Ya. S. Dubnov, Errores en las Demostraciones Geometricas, Rubinos, Madrid, Spain, 1993. (in Spanish)
• Common errors in mathematics