Pythagoras Theorem
The theorem is famous and can be proved by both algebraic and geometric method.
Algebraic Method
Consider the following figure and calculate the total area:
Click to enlarge.
Click to enlarge.
For more information, there are a few links to the proofs of Pythagoras theorem.
Wikipedia http://en.wikipedia.org/wiki/Pythagorean_theorem
http://jwilson.coe.uga.edu/emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html