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At an American Mathematical Society meeting, high school students presented a proof of the Pythagorean theorem that used trigonometry—an approach that some once considered impossible

Two high school students have proved the Pythagorean theorem in a way that one early 20th-century mathematician thought was impossible: using trigonometry.

Calcea Johnson and Ne’Kiya Jackson, both at St. Mary’s Academy in New Orleans, announced their achievement last month at an American Mathematical Society meeting. “It’s an unparalleled feeling, honestly, because there’s just nothing like it, being able to do something that ... people don’t think that young people can do,” Johnson told WWL-TV, a New Orleans CBS affiliate.

If verified, Johnson and Jackson’s proof would contradict mathematician and educator Elisha Loomis, who stated in his 1927 book The Pythagorean Proposition that no trigonometric proof of the Pythagorean theorem could be correct. Their work joins a handful of other trigonometric proofs that were added to the mathematical archives over the years. Each sidestepped “circular logic” to prove the pivotal theorem. So what exactly is a trigonometric proof of the Pythagorean theorem, and why was Loomis so closed off to the idea?

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