Two New Orleans high school students, Calcea Johnson and Ne’Kiya Jackson, have sparked significant interest in the mathematical community.
On March 18, Johnson and Jackson delivered a presentation titled “An Impossible Proof of Pythagoras” at the American Mathematics Society’s Spring Southeastern Section Meeting at Georgia Tech in Atlanta.
The St. Mary’s Academy seniors revealed a proof that demonstrated the Pythagorean theorem using trigonometry without relying on circular logic. Despite prior beliefs that this was impossible, their findings were reported by local CBS affiliate 4WWL.
At a regional conference in late 2022, the students introduced a new twist on proving the Pythagorean Theorem. For nearly 2,000 years, it was thought impossible to prove the theorem with trigonometry. However, Johnson and Jackson’s work has challenged this long-held belief.
The Pythagorean Theorem, a fundamental aspect of geometry, posits that the square of the hypotenuse (the side opposite the right angle) in a right triangle equals the sum of the squares of the other two sides. Despite the existence of hundreds of proofs, none had used trigonometry, which heavily depends on the theorem itself.
The apparent contradiction intrigued Johnson and Jackson during a school-wide math competition. The bonus question asked them to construct a new proof using trigonometry. Motivated by curiosity and the challenge (with a competitive prize as an added incentive), they set out on a path that could reshape mathematical history.
Their method involved reinterpreting trigonometric functions within the right triangle. Though not entirely avoiding circular logic, they discovered a way to employ trigonometry without directly depending on the Pythagorean Theorem.
The mathematical community is buzzing with anticipation. As the proof undergoes thorough peer review, its potential implications are causing excitement. New insights into well-established concepts could pave the way for unexpected advancements.
