Construction to prove the Pythagorean theorem.The area of the inner square is c ^{2}, the area of the outer square is (a+b)^{2}, and the area of each triangle is (1/2)(ab).Knowledge of the areas, and a little math, gives the theorem. (Drawing by the author using Inkscape.) |

US President James Garfield's proof of the Pythagorean theorem.The proof is made by equating the area of the trapezoid to the combined area of the triangles. Although a high school student should be able to complete the proof when given this construction, you can find the solution here. Inkscape illustration by the author. |

Leonardo's drawing of a rhombicuboctahedron, an Archimedean solid formed from squares and triangles.(Woodcut from Pacioli's De divina proportione (Venice, 1509).Via Wikimedia Commons.) |

Geometrical construction for "Leonardo's" proof of the Pythagorean theorem. (Drawn by the author using Inkscape.) |

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