Dating by olympiads
Below is a collection of 118 approaches to proving the theorem.Many of the proofs are accompanied by interactive Java illustrations. C.) or someone else from his School was the first to discover its proof can't be claimed with any degree of credibility. C.) by an early 20th century professor Elisha Scott Loomis.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.Curiously, nowhere in the book does Loomis mention Euclid's VI.31 even when offering it and the variants as algebraic proofs 1 and 93 or as geometric proof 230. I'll give an example of their approach in proof #56.
Obviously the resulting shape is a square with the side c and area c². (A variant of this proof is found in an extant manuscript by Thâbit ibn Qurra located in the library of Aya Sofya Musium in Turkey, registered under the number 4832. The proof itself starts with noting the presence of four equal right triangles surrounding a strangely looking shape as in the current proof #2.
There is a small collection of rather elementray facts whose proof may be based on the Pythagorean Theorem.