Two High School Students Present New Proof For Pythagoras' Theorem

Two high school students presented their Pythagoras' Theorem proof on March 18^th at the American Mathematical Society's Annual Southeastern Conference. (Image Credit: WWL)

Two 17-year-old New Orleans high school students say they have solved Pythagoras' Theorem that scholars have tried to prove for 2,000 years. Ne'Kiya Jackson and Calcea Johnson attended the American Mathematical Society's Annual Southeastern Conference and presented their evidence proving the Pythagorean Theorem using trigonometry. They were the only high schoolers attending the March 18th meeting in Georgia. Math researchers from various institutes also attended the meeting. 

"In the 2,000 years since trigonometry was discovered, it's always been assumed that any alleged proof of Pythagoras's Theorem based on trigonometry must be circular," the students wrote in the abstract. "In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that 'There are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem. But that isn't quite true: in our lecture, we present a new proof of Pythagoras's Theorem, which is based on a fundamental result in trigonometry — the Law of Sines — and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1." This meant they claimed to prove the theorem with trigonometry without applying circular logic. 

The theorem is used in everyday fields, including construction, architecture, spaceflight, computer science, and navigation. It states, "the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides." Schools have taught the notation to students in geometry classes: a²+b²=c².

The American Mathematical Society has encouraged both students to submit their groundbreaking proof for peer review. Jackson told WWL, a New Orleans TV station, that presenting her and Jackson's proof was an "unparalleled feeling." "There's nothing like it – being able to do something that people don't think that young people can do," Johnson said. "You don't see kids like us doing this – it's usually, like, you have to be an adult to do this."

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