It takes a special kind of student to outsmart 2,000 years of mathematicians — but New Orleans teenagers Calcea Johnson and Ne’Kiya Jackson are two of them.
Calcea Johnson and Ne’Kiya Jackson just gave a presentation to the American Mathematical Society’s Annual Southeastern Conference.
The students cracked the code of an impossible math problem by demonstrating that Pythagoras’ Theorem can be proven without trigonometry–the study of triangles–something that many believed was impossible.
Johnson and Jackson recently presented their evidence to a peer-reviewed journal that is published by a prominent US mathematical research organization.
Legions of schoolchildren have learned the notation summarizing the theorem in their geometry classes: A2+B2=C2.
“In the 2000 years since trigonometry was discovered, it’s always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular,” said Johnson and Jackson’s 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.”
It might not surprise you to hear they were the only high school students in the room.
“It’s really an unparalleled feeling, honestly, because there’s just nothing like being able to do something that people don’t think young people can do,” Calcea said. “A lot of times you see this stuff, you don’t see kids like us doing it.
They attend St. Mary’s Academy, a private Catholic K-12 school in New Orleans, Louisiana run by the Sisters of the Holy Family. Founded in 1867, St. Mary’s is one of the oldest Black Catholic schools in the country
If you need a refresher on Pythagorean Theory, you’re not alone.
Johnson and Jackson explained it like this: Basically, trigonometry is based on Pythagoras’ Theorem, but using trigonometry to prove Pythagoras’s Theorem is what’s known as circular logic.
Circular reasoning is considered a pragmatic defect in an argument where the premise is just as much in need of proof as the conclusion, because in logic, an idea can’t prove itself.
Johnson and Jackson were reportedly the only two high schoolers to give presentations at the American Mathematical Society south-eastern chapter’s semi-annual meeting in Georgia, a gathering attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech.
Describing her experience as an “unparalleled feeling,” Jackson said: “We have really great teachers.”
“There’s nothing like it – being able to do something that people don’t think that young people can do,” said Johnson. “You don’t see kids like us doing this – it’s usually, like, you have to be an adult to do this.”
The girls are on their way to earning STEM degrees, with plans to study environmental engineering and biochemistry.
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