In March 2023, Calcea Johnson and Ne'Kiya Jackson, two high school students, proved the Pythagorean theorem in a way that was previously thought to be impossible: using trigonometry. In the 2,000 years since trigonometry was discovered, it has always been assumed that any alleged proof of the Pythagorean theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis), the author states that "There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem." However, that isn't entirely accurate. The authors came up with a new proof of the Pythagorean theorem that is based on a fundamental result in trigonometry—the Law of Sines—and they demonstrate that the proof is independent of the Pythagorean identity sin²x + cos²x = 1.

C-K Shene analysis of Calcea Johnson and Ne'Kiya Jackson proof is a great paper for your summer reading list 📚 :