Louisiana High School Seniors Say They Discovered a New Proof for 2,000-Year-Old Math Theorem

Calcea Johnson and Ne’Kiya Jackson believe they can prove the Pythagorean Theorem using trigonometry — and are being encouraged to submit their work for peer review

Two Louisiana students claim to have found a new discovery for a math problem that has intrigued mathematicians for 2,000 years.

According to CBS affiliate WWL-TV, St. Mary’s Academy students Calcea Johnson and Ne’Kiya Jackson believe they have found a new proof for Pythagorean Theorem that uses trigonometry without resorting to circular logic.

The pair recently presented their findings at the American Mathematical Society’s Annual Southeastern Conference.

“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,” Johnson told the news station. “A lot of times you see this stuff, you don’t see kids like us doing it.”

Per The Guardian, Johnson and Jackson were the only high school students to present at the event, typically attended by university researchers.

The Pythagorean Theorem states that three sides of a right-angled triangle can be expressed by the formula a2+b2=c2.

But it has broadly been accepted that there is no way to define the theorem using trigonometry — which is what Jackson and Johnson claim they have now done.

In an abstract posted on the American Mathematical Society’s website, the two said they used the Law of Sines — which is used to find angles of a general triangle — in their findings.

“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,” the pair said. “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.'”

They continue: “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.”

According to Insider, academics have made similar claims.

Per The Guardian, the American Mathematical Society’s Executive Director Catherine Roberts is encouraging the two teens to submit their findings to a peer-reviewed journal to “determine whether their proof is a correct contribution to the mathematics literature.”

“We encourage them to continue their studies in mathematics,” Roberts continued.

While speaking to WWL-TV, Johnson said their instructors helped inspire their presentation.

“Our slogan is ‘No Excellence Without Hard Labor,'” she shared. “So, they definitely push us.”

Jackson added: “We have really great teachers.”

Source: https://people.com/human-interest/teens-claim-discovered-new-proof-math-pythagorean-theorem-2000-years-old/