NEW ORLEANS (WGNO) – Two students at a school in New Orleans have presented evidence of a mathematical discovery that scholars have been trying to prove for 2,000 years.

School officials at St. Mary’s Academy say Calcea Johnson and Ne’Kiya Jackson, both 17, attended the American Mathematical Society’s Annual Southeastern Conference where they said they had found a way to prove the Pythagorean theorem using trigonometry and without using circular logic.

“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 teenage authors wrote in the abstract of their presentation a the conference. “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.”

Used to calculate the side lengths of a right triangle, this type of proof for the Pythagorean theorem was thought to be impossible. The standard Pythagorean theorem is used on an everyday basis in professions like architecture, building construction, navigation, spaceflight, computer sciences, and more.

Johnson and Jackson first became interested in Pythagoras’ theorem when they entered a math contest created to spark students’ further interests in the field, according to St. Mary’s. The study led them to believe the theory’s original proof was inaccurate.

The students made their groundbreaking lecture to mathematical scholars on March 18 in Atlanta, Georgia.

The two students, both 17, presented their findings at the American Mathematical Society’s Annual Southeastern Conference on March 18, 2023. (St. Mary’s Academy New Orleans)

Several alumni from St. Mary’s Academy have since congratulated the girls on their presentation.

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“I am in awe of these wonderful young ladies!” wrote one supporter in response to a Facebook post shared by the school.

“Two phenomenal little sisters doing phenomenal work!” another wrote. “Keep soaring Maryites!!!”