00:03The 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,
00:11especially with regards to engineering, has historically been impossible to prove with
00:15trigonometry. That is, despite the theorem being integral to trigonometry itself.
00:19With mathematician Elijah Loomis writing famously in 1927, quote,
00:24there are no trigonomic proofs, because all the fundamental formulae of trigonometry are
00:28themselves based upon the truth of the Pythagorean Theorem. However, now two high school students
00:33have done exactly that, 10 times over. This is Nakia Jackson and Kelsia Johnson,
00:38the two who figured the whole thing out. They say it wasn't easy and at several points they
00:42wanted to give up, but eventually used the law of signs 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. They then took it further and proved it nine more
00:55times. Their 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 students
01:05on the field.
