An ancient generalization of the Pythagorean theorem
SMRTR summary
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.
SMRTR provides this summary for quick context. The original article belongs to John D. Cook.
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