Louisiana Teens Publish 10 New Trigonometric Proofs of Pythagorean Theorem

New Orleans, LA – Ne'Kiya Jackson and Calcea Johnson, two former high school students from St. Mary's Academy, have published ten new trigonometric proofs for the Pythagorean Theorem in the American Mathematical Monthly. This achievement builds upon their initial discovery made in 2022, which challenged a long-held mathematical assertion that such proofs were impossible without circular reasoning. Their work has garnered significant attention in the mathematical community.

For over 2,000 years, the Pythagorean Theorem (a² + b² = c²) has been extensively proven using geometry and algebra. However, mathematician Elisha Loomis asserted in 1927 that a trigonometric proof was impossible due to the inherent circular logic, as many trigonometric identities are themselves derived from the theorem. Prior to Jackson and Johnson's work, only two other independent trigonometric proofs existed.

The journey began when Jackson and Johnson, then seniors at St. Mary's Academy, tackled a bonus question in a school math contest that offered a $500 prize. The challenge was to create a new trigonometric proof of the theorem. Despite initial skepticism and the difficulty of the task, they independently developed their first proofs.

After presenting their initial findings at an American Mathematical Society meeting in March 2023, the duo embarked on the "daunting task" of publishing their work in a peer-reviewed journal. This process led them to discover additional proofs. Calcea Johnson stated, "It was important to me to have our proofs published to solidify that our work is correct and respectable."

Their published paper outlines five new proofs and a method that can generate five more, totaling ten distinct trigonometric proofs. Mathematician Álvaro Lozano-Robledo of the University of Connecticut noted that one of their proofs, involving filling a larger triangle with an infinite sequence of smaller ones, "looks like nothing I’ve ever seen." Their work demonstrates that trigonometric terms can be defined in ways that allow for non-circular proofs.

Now college students—Jackson studying pharmacy at Xavier University of Louisiana and Johnson environmental engineering at Louisiana State University—their contributions are expected to inspire future mathematicians. Jackson hopes their proofs will encourage students to "see that obstacles are part of the process. Stick with it, and you might find yourself achieving more than you thought possible."