For over two millennia, mathematicians have tirelessly sought to demonstrate the Pythagorean Theory of trigonometry using logical reasoning devoid of circularity. However, amidst numerous unsuccessful attempts, a glimmer of hope has emerged courtesy of two exceptional students from New Orleans East.
Calcea Johnson and Ne’Kiya Jackson recently astounded the audience at the American Mathematical Society’s Annual Southeastern Conference held in March, where they stood out as the sole high school participants, as reported by WWL-TV.
“It’s truly an indescribable feeling, to be honest, because there’s nothing quite like the satisfaction of accomplishing something that is often deemed beyond the capabilities of young individuals,” expressed Calcea with enthusiasm. “Most of the time, when you encounter these concepts, you don’t witness young people like us actively engaging with them.”
The talented duo went on to elucidate that the Pythagorean Theorem, which asserts that the three sides of a right-angled triangle can be represented by the formula a² + b² = c², forms the foundation of trigonometry. Paradoxically, employing trigonometry to prove Pythagoras’ Theorem falls into the realm of circular logic.
Per PEOPLE, two said they used the Law of Sines — which is used to find angles of a general triangle — in their findings.
“In the span of 2,000 years since the discovery of trigonometry, it has been widely assumed that any purported proof of Pythagoras’s Theorem based on trigonometry would inevitably lead to circular reasoning,” shared the determined pair. “In fact, within the pages of ‘The Pythagorean Proposition’ by Elisha Loomis, acknowledged as the most extensive compilation of proofs, the author unequivocally asserts that ‘There are no trigonometric proofs, as the very foundations of trigonometry are built upon the truth of the Pythagorean Theorem.'”
Catherine Roberts, the Executive Director of the American Mathematical Society, wholeheartedly encourages the two young talents to submit their remarkable findings to a peer-reviewed journal, aiming to assess the validity of their proof as a valuable addition to the mathematical literature.
The gifted students, who are enrolled at St. Mary’s Academy in New Orleans, attribute their success to the unwavering support of their exceptional teachers. They also proudly emphasize the motto of their esteemed private Catholic institution, which states, “No Excellence Without Hard Labor.”