tells of an experiment he ran in one of his geometry classes.He drew a right triangle on the board with squares on the hypotenuse and legs and observed the fact the the square on the hypotenuse had a larger area than either of the other two squares.Actually, for some people it came as a surprise that anybody could doubt the existence of trigonometric proofs, so more of them have eventaully found their way to these pages.

Thus the area of ΔAEC equals half that of the rectangle AELM.The theorem is of fundamental importance in Euclidean Geometry where it serves as a basis for the definition of distance between two points.It's so basic and well known that, I believe, anyone who took geometry classes in high school couldn't fail to remember it long after other math notions got thoroughly forgotten.There is a small collection of rather elementray facts whose proof may be based on the Pythagorean Theorem.There is a more recent page with a list of properties of the Euclidian diagram for I.47.Below is a collection of 118 approaches to proving the theorem.

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