About: Adrakhonic Theorem   Sponge Permalink

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The DU displays a visual proof of the Pythagorean Theorem that is unusual, but not wholly unintelligible. Whereas two popular proofs rely on the juxtaposition of similar shapes, and one relies on the projection of rectangles and parallelograms of equal bases, the DU proof perhaps demonstrates a basic knowledge of trigonometry.

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  • Adrakhonic Theorem
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  • The DU displays a visual proof of the Pythagorean Theorem that is unusual, but not wholly unintelligible. Whereas two popular proofs rely on the juxtaposition of similar shapes, and one relies on the projection of rectangles and parallelograms of equal bases, the DU proof perhaps demonstrates a basic knowledge of trigonometry.
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abstract
  • The DU displays a visual proof of the Pythagorean Theorem that is unusual, but not wholly unintelligible. Whereas two popular proofs rely on the juxtaposition of similar shapes, and one relies on the projection of rectangles and parallelograms of equal bases, the DU proof perhaps demonstrates a basic knowledge of trigonometry. More than one proof can be based on the DU diagram. One of them is the proof from Euclid's Elements. Another uses the formula for area of a right triangle and that the the two other triangles each appear twice after rotation by a right angle so each copy has the same area. One gets a system of equations. Eliminating the areas of the two triangles that each appear twice and simplifying yields the Pythagorean formula.
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