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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.
Which says that the area AC² of the square on side AC equals the area of the rectangle AELM. Calderhead ( We start with two squares with sides a and b, respectively, placed side by side. The construction did not start with a triangle but now we draw two of them, both with sides a and b and hypotenuse c.
The square has a square hole with the side and a hole with the side c.The is the statement that the sum of (the areas of) the two small squares equals (the area of) the big one.In algebraic terms, a² b² = c² where c is the hypotenuse while a and b are the legs of the triangle.These four triangles correspond in pairs to the starting and ending positions of the rotated triangles in the current proof.This same configuration could be observed in a proof by tessellation.) Now we start with four copies of the same triangle.