US Teens Come Up With 5 New Ways Of Proving Pythagoras Theorem Using Trigonometry

Two US college students, who discovered a new way to prove Pythagoras' famous 2,000-year-old theorem in 2022 have now come up with five different ways of solving the problem using trigonometry. Their new solutions have been published in the journal American Mathematical Monthly. The famous theorem is summarised as a²+b²=c^2, which helps in finding the length of a right-angled triangle. Essentially, it means that the square of the longest side (the hypotenuse) is equal to the squares of the two shorter sides added together.

Over the years, many mathematicians have tried to prove the theorem using algebra and geometry but using trigonometry was long believed impossible. However, Calcea Johnson and Ne'Kiya Jackson, astonished everyone with their achievements as high school kids when they solved the problem without resorting to circular reasoning-a feat managed twice previously by professional mathematicians.

As college students, they have now breached a new frontier by not only coming up with five ways to solve the puzzle but also with a method that reveals five other proofs - totalling ten proofs altogether. Only one proof was previously presented, meaning the remaining nine are totally new.

"I was pretty surprised to be published. I didn't think it would go this far," Jackson said in a news release.

"It's very exciting for me, because I know when I was growing up, STEM [science, technology, engineering, and math] wasn't really a cool thing. So the fact that all these people actually are interested in STEM and mathematics really warms my heart and makes me really excited for how far STEM has come."

Also read | US Teens Discover New Proof For The Pythagoras' Theorem, Stun Mathematicians

Della Dumbaugh, the editor of the journal that published the groundbreaking research said she was "not only honoured that the authors trusted the Monthly with their important results" but also deeply gratified by the "behind-the-scenes work of the Editorial Board". Dumbaugh was referring to Grant Cairns, one of the Editorial Board members, who sanitised Johnson and Jackson's work to make it look more presentable on scientific papers.

Despite being great at maths, neither of them is pursuing a career in the subject. While Jackson is a student in the pharmacy department of Xavier University in New Orleans, Johnson is studying environmental engineering at Louisiana State University.