William Dunham showed me this elegant symmetric proof of Heron's formula by Bernard Oliver http://johnng.inscyber.net/proof-without-words-heron.pdf …pic.twitter.com/A4BQqzuMN0
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@stevenstrogatz That deus-ex-machina half-angle identity is what frustrates me here. Why would anyone ever think of it, or its proof?
.@MathPrinceps it's easier to prove with Euler's formula. Use alpha+beta+gamma=pi, divide by 2, then look at Re and Im part of e^(i pi/2)
@stevenstrogatz Then Heron follows from "The sum of the squares on the sides of a parallelogram equals the sum of the diagonal squares."
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