Two New Orleans high school seniors who claim to have used trigonometry to prove Pythagorean’s theorem – something academics thought impossible for two millennia – are being encouraged by a leading American mathematics research organization to submit their work to a peer-reviewed journal.
Calcea Johnson and Ne’Kiya Jackson of St. Mary’s Academy, presented their findings at the American Mathematical Association Southeast biannual meeting in Georgia.
They were the only high school students present at the meeting, which was attended by math researchers from institutions such as the Universities of Alabama, Georgia, Louisiana, Ohio State, Oklahoma and Texas Tech. And they talked about discovering a new proof for the Pythagorean Theorem.
A 2,000-year-old theorem says that the sum of the squares of two of the shortest sides of a right triangle is equal to the square of the hypotenuse – the third and longest side opposite the right triangle. In geometry class, scores of schoolchildren learned the notation that sums up the theory: a2 + b2 = c2.
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As noted in the summary of Johnson and Jackson’s March 18 Mathematical Society presentation, trigonometry—the study of triangles—is based on theory.
Since discovering this particular area of study, mathematicians have confirmed that any purported proof of the Pythagorean Theorem using trigonometry constitutes a logical fallacy known as circular reasoning, a term used when someone is trying to come up with an idea using to validate the idea itself.
Johnson and Jackson’s abstract adds that the book containing the largest known proof theorem for the theorem – Elisha Loomis’ Pythagorean Proposition – “states categorically that there are no trigonometric proofs because all the basic formulas of trigonometry rest on the truth based on Pythagoras’ theorem.”
But the simple counter: “It’s not right.” The duo states: “We present a new proof of the Pythagorean theorem based on a fundamental result of trigonometry – the law of sines – and show that the proof is independent of the Pythagorean trigonometric identity sin2x + cos2x = 1.” In short, they can prove the theorem using trigonometry and without resorting to circular reasoning.
The Johnsons told New Orleans television station WWL that it was “an unparalleled feeling” for her and Jackson’s work alongside university researchers.
