US teens prove 2000-years-old Pythagoras's theorem through trigonometry

An infamous US mathematical research organisation 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 Pythagoras’s theorem, which academics have believed to be impossible for two millennia.

Students from St. Mary’s Academy, Calcea Johnson and Ne’Kiya Jackson, recently presented their research at the semi-annual conference of the American Mathematical Society’s South-Eastern Chapter in Georgia.

According to reports, they were the only two high school students to speak at the meeting, which was attended by mathematicians from universities such as Alabama, Georgia, Louisiana State, Ohio State, Oklahoma, and Texas Tech.

Additionally, they discussed how they had found a fresh evidence for the Pythagorean theorem.

The 2,000-year-old theorem stated that the square of the hypotenuse, or third, longest side opposite the right angle of a right triangle, matches the sum of the squares of the two shorter sides.

In their geometry classes, countless students learned the notation expressing the theory as a2+b2=c2.

Trigonometry, the study of triangles, relies on the theorem, as stated in the abstract of Johnson and Jackson’s presentation to the mathematical society on March 18. Since that particular area of study was found, mathematicians have insisted that any assertion that the Pythagorean theorem can be proved using trigonometry is false.

This claim is known as circular reasoning, which is the term for when someone attempts to prove an idea by using the same argument that they are using to support it.

The Pythagorean Proposition by Elisha Loomis, which contains the largest known collection of theorem proofs, “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,” according to Johnson and Jackson’s abstract.

That isn’t quite true, the idea responds. “We present a new proof of Pythagoras’ Theorem based on a fundamental trigonometric result – the Law of Sines – and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1,” the pair claims.

In other words, they could demonstrate the theorem without using circular logic by using trigonometry.

To show her and Jackson’s work alongside academic researchers was a “unparalleled feeling,” Johnson told the New Orleans television news station WWL.

Being able to accomplish something that others don’t believe young people are capable of is unparalleled, Johnson told the station. Usually, you have to be an adult to do this, so you don’t see toddlers like us doing it.

The two students at St. Mary’s All-Girls School in New Orleans’ Plum Orchard neighbourhood expressed gratitude to their instructors for pushing them to achieve something that mathematicians had deemed impossible. St. Mary’s motto is “No excellence without hard labour.”

In an interview with WWL that was published on Thursday, Jackson stated, “We have really great teachers.”

According to WWL, Jackson and Johnson are on track to finish this spring, and they want to work in both biochemistry and environmental engineering.

Administrators from St. Mary’s Academy did not right away reply to a request for comment on Friday. Judge Dana Douglas, the first Black woman to preside over the federal fifth circuit court of appeals, and well-known restaurateur Leah Chase are notable graduates of the institution.

Even at their relatively young ages, Catherine Roberts, executive director for the American Mathematical Society, advised the St. Mary’s students to consider having their work evaluated by a peer-reviewed publication.

“Members of our community can examine their results to ascertain whether their proof is an accurate addition to the mathematics literature,” said Roberts, whose organisation organises scientific conferences and releases scholarly journals.

Additionally, Roberts stated that members of the American Mathematical Society “celebrate these early career mathematicians for sharing their work with the larger mathematics community.”

We urge them to pursue further mathematics education, Roberts continued.