UNITED STATES: An influential American mathematical research group is encouraging two New Orleans high school seniors to submit their work to a peer-reviewed publication after they claim to have used trigonometry to demonstrate the Pythagorean theorem, which scholars have believed to be impossible for two millennia.
Calcea Johnson and Ne’Kiya Jackson, both students at St. Mary’s Academy, recently presented their research at a meeting of the American Mathematical Society’s South-Eastern Chapter in Georgia.
They were the only two high school students to speak at the meeting, which included math experts from Alabama, Georgia, Louisiana State, Ohio State, Oklahoma, and Texas Tech. They also talked about how they discovered a new proof for the Pythagorean theorem.
According to the 2,000-year-old theory, the square of the hypotenuse, or third, longest side of a right triangle, which is located across from the right angle, is equal to the sum of the squares of the shorter sides. a2+b2=c2 is the notation that sums up the theorem, which countless students have studied in geometry lectures.
As stated in the abstract of Johnson and Jackson’s 18 March presentation, mathematicians have insisted that since that particular field of study (Trignometry) was discovered, any assertion that the Pythagorean theorem can be proved using trigonometry is illogical and guilty of circular reasoning, which is the attempt to prove one’s proposition by using the proposition itself as a basis.
The Pythagorean Proposition by Elisha Loomis has the largest known collection of theorem proofs. According to the abstract by Johnson and Jackson, the book “states flatly that there are no trigonometric proofs because all the basic formulas of trigonometry are based on the truth of the Pythagorean theorem.”
The abstract responds, “That isn’t entirely true,” though. The two claim that they have “presented a new proof of Pythagoras’s Theorem based on a fundamental trigonometric finding, the Law of Sines.”
Their work shows that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1. In other words, they were able to demonstrate the theorem using trigonometry and without the use of circular reasoning.
The two pupils at St. Mary’s All-Girls School in New Orleans’ Plum Orchard neighbourhood expressed gratitude to their professors for pushing them to achieve something that mathematicians had deemed impossible. St. Mary’s motto is “No excellence without hard labour.”
An inquiry for comment on Friday was not immediately answered by St. Mary’s Academy administration. Leah Chase, a well-known restaurateur, and Judge Dana Douglas, the first Black woman to preside over the federal Fifth Circuit Court of Appeals, are both graduates of the institution.
Even at their very young ages, the St. Mary’s kids were urged to consider having their work reviewed by a peer-reviewed journal by Catherine Roberts, executive director of the American Mathematical Society.
The American Mathematical Society’s members, according to Roberts, “honour these early career mathematicians for sharing their work with the wider mathematics community.”
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