The Pythagorean Theorem
In any right-angled triangle, a² + b² = c² — the squares of the two short sides add up to the square of the long one (the hypotenuse).
Origin
Named after Pythagoras (c. 570–495 BCE), though Babylonian tablets show the relationship was known a thousand years before him. Pythagoras and his followers were a strange semi-cult — they believed numbers were the substance of reality, refused to eat beans, and may or may not have drowned a member who proved the existence of irrational numbers. There are over 400 known proofs of the theorem, including one by a future US president (James Garfield, 1876).
Modern usage
The one piece of geometry most adults still remember. Used as the canonical example of 'something I learned in school' and the standard joke headstone for math itself. Shows up implicitly any time you measure a diagonal — TV sizes, screens, room layouts, distance on a flat map.
In the wild
I can do Pythagoras and that's about it.— common usage
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