American teenagers came up with 5 new ways to prove the Pythagorean theorem using trigonometry

The well-known theorem is summarized as a2+b2=c2

Two American college students who in 2022 discovered a new way to prove the famous 2,000-year-old Pythagorean theorem have now come up with five different ways to solve the problem using trigonometry. Their new solutions were published in the American Mathematical Monthly. The known theorem is generalized as a²+ b²=c^2,which helps to find the length of a right triangle. Essentially, this 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 tried to prove the theorem using algebra and geometry, but the use of trigonometry was long considered impossible. However, Kalsea Johnson and Ne’Kia Jackson stunned everyone with their accomplishments as high school students when they solved a problem without resorting to circular reasoning, a feat that had only been accomplished twice before by professional mathematicians.

As college students, they have now broken a new frontier by not only coming up with five ways to solve the puzzle, but also coming up with a method that reveals five other pieces of evidence – a total of ten pieces of evidence. Previously, only one confirmation was presented, that is, the remaining nine are completely new.

“I was very surprised by the publication. I didn’t think it would go this far,” Jackson said in a press release.

“It’s really exciting for me because I know that when I was growing up, STEM (Science, Technology, Engineering and Math) wasn’t a cool thing. So the fact that all these people are actually interested in STEM and math really warms my heart and makes me really excited about how far STEM has come.”

Della Dumbo, the editor of the journal that published the ground-breaking study, said she was “not only honored that the authors have trusted the Monthly with their important findings,” but also deeply satisfied with the “behind-the-scenes work of the editorial board.” Dumbo was referring to Grant Kearns, one of the editorial board members who cleaned up Johnson and Jackson’s work to make it more presentable in scholarly articles.

Although they are excellent at mathematics, neither of them intends to pursue a career in this subject. While Jackson is studying pharmacy at Xavier University in New Orleans, Johnson is studying environmental engineering at Louisiana State University.