Two HS Students find the First Trigonometric Proof of the Pythagorean Theorem

This is a wonderful story.

Ne’Kiya Jackson & Calcea Johnson, two high school students, have found new proofs of the Pythagorean Theorem and published them in The American Mathematical Monthly (Volume 131, Issue 9, November 2024). The article is titled, “Five or Ten New Proofs of the Pythagorean Theorem.” This is the first time that trigonometry has been used to prove the Pythagorean Theorem (and it was previously believed to be impossible).

In The Pythagorean Proposition, a 1927 book by Elisha Scott Loomis, Loomis catalogs over 370 proofs of the Pythagorean Theorem (none of which used trig). I always like to add that one proof of the Pythagorean Theorem was written by US President James Garfield.

Jackson and Johnson presented at an AMS conference first. Then it got bigger and bigger and lead to a significant publication in the Monthly. Kudos to their teachers, and others, for encouraging them and helping the process along the way.

This story has been covered widely in the media. Here are some links.

I believe Ne’Kiya Jackson and Calcea Johnson received the Gumbo Coalition Award on May 13, 2023.

Link the the Actual Article

Five or Ten New Proofs of the Pythagorean Theorem, from The American Mathematical Monthly can be found here and downloaded. It is very readable and well-written. Also note the Editor’s Note which follows the article at the end.

Significance

This is a wonderful story, because it shows that anyone (even young people in high school) can come up with a contribution to mathematics, it involves the Pythagorean Theorem which is one of the most beautiful and pervasive theorems in all of mathematics, and the way the professional (and even media) community have helped graciously share the story.