Ne’Kiya Jackson and Calcea Johnson, two high school classmates, have made waves in the mathematical world by unveiling 10 new trigonometric proofs of the Pythagorean theorem. This groundbreaking achievement was published in the American Mathematical Monthly on October 28, marking a significant milestone in the field of mathematics.
The Pythagorean theorem, a^2 + b^2 = c^2, has been a fundamental concept in geometry for over 2,000 years. While the theorem has been proven multiple times using algebra and geometry, trigonometry has long been considered incapable of providing a proof due to circular logic. However, Jackson and Johnson defied the odds and presented their first trigonometry-based proof in 2022 while still high school seniors at St. Mary’s Academy in New Orleans.
Their initial success inspired them to continue their research, leading to the development of additional proofs. After presenting their work at an American Mathematical Society meeting in March 2023, the duo embarked on the challenging task of publishing their findings in a peer-reviewed journal. Despite the obstacles, including learning to code in LaTeX, they remained determined to see their work through to publication.
One of the standout proofs in their collection involves filling a larger triangle with an infinite sequence of smaller triangles and using calculus to determine the lengths of the larger triangle’s sides. This innovative approach caught the attention of mathematician Álvaro Lozano-Robledo, who praised the students’ creativity and originality.
In their published paper, Jackson and Johnson also provide a lemma that offers a clear path to discovering five additional proofs. By focusing on a specific method of defining trigonometric terms, they were able to develop unique proofs for different types of right triangles.
With their work now available to the mathematical community, Jackson and Johnson hope to inspire other students to persevere in the face of challenges. Their journey serves as a reminder that with dedication and determination, even high school students can make significant contributions to the field of mathematics.
Overall, their achievement opens up new possibilities for further exploration and discussion within the mathematical community. By sharing their innovative proofs, Jackson and Johnson have sparked a new wave of mathematical conversations and potential discoveries.
