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Two high school students solved a 2k-year-old math puzzle
- WCSTombs 2y agoThe Pythagorean Theorem is one of the oldest theorems in mathematics, and it is also the one with the largest number of known proofs. > When Calcea and Ne'Kiya set out to create a new Pythagorean Theorem proof, they didn't know that for thousands of years, one using trigonometry was thought to be impossible. In 2009, mathematician Jason Zimba submitted one, and now Calcea and Ne'Kiya are adding to the canon. A non-circular proof using trigonometry _would_ be interesting, but I didn't find the proof given or linked anywhere in the article.
- WCSTombs 2y agoActually they do start talking about it in the video at the top of the page, but they don't complete it.
- tocs3 2y agoHere is little more technical discussion. https://publications.azimpremjiuniversity.edu.in/4877/1/01-Shailesh_TwoNewProofsOfPythagoreanTheorem-I_Final.pdf https://publications.azimpremjiuniversity.edu.in/4877/1/01-S...
- WCSTombs 2y agoThank you, that's truly excellent! And although it is a little bit technical and more complex than the more standard proofs, it is exactly what it claims to be, a non-circular trigonometric proof of the Pythagorean Theorem. They use a key trigonometric identity sin(2*a) = 2*sin(a)*cos(a), which indeed is quite easy to prove without assuming the Pythagorean Theorem.