Two U.S. high school students, Ne’Kiya Jackson and Calcea Johnson, achieved the seemingly impossible in 2023 by publishing 10 new proofs of the Pythagorean theorem, a rule central to trigonometry. Historically, it was believed impossible to prove the theorem using trigonometry due to the circular reasoning involved—trigonometric formulas themselves rely on the truth of the Pythagorean theorem. However, Jackson and Johnson succeeded by clarifying two different versions of trigonometry and using the Law of Sines to avoid circular logic. Their achievement challenges the long-held belief and provides fresh insights into a fundamental mathematical principle.
