SMRTR Science & EngineeringOct 30, 2025John D. Cook

An ancient generalization of the Pythagorean theorem

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Apollonius of Perga discovered an ancient theorem that extends the famous Pythagorean theorem to any triangle, not just right triangles. His formula states that for any triangle with a midpoint on one side, the sum of squares of two sides equals twice the sum of squares of half the third side and the median. When applied to right triangles, Apollonius's theorem reduces to the standard Pythagorean theorem, demonstrating its broader mathematical significance.

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