The Pythagorean Theorem explains how three sides of a right-triangles work together. However, despite being an integral to trigonometry it cannot be explained by it, that is until now.
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00:00The Pythagorean theorem explains how three sides of a right triangle work together.
00:07It's an ancient mathematical principle, though while extremely useful in modern day especially
00:11with regards to engineering, has historically been impossible to prove with trigonometry.
00:16That is despite the theorem being integral to trigonometry itself.
00:19With mathematician Elijah Loomis writing famously in 1927, quote, there are no trigonomic proofs
00:25because all the fundamental formulae of trigonometry are themselves based upon the truth of the
00:30Pythagorean theorem.
00:31However now two high school students have done exactly that, ten times over.
00:36This is Nakia Jackson and Kelsia Johnson, the two who figured the whole thing out.
00:40They say it wasn't easy and at several points they wanted to give up, but eventually used
00:44the law of sines to get around previous roadblocks.
00:47In one of their proofs they used multiple smaller triangles within another larger one
00:50and used calculus to measure the smaller triangles.
00:53They then took it further and proved it nine more times.
00:56Their results are now published in American Math Monthly with the journal's editor-in-chief
01:00saying about it, their results call attention to the promise of the fresh perspective of
01:04students on the field.