Proof that eluded math for millennia… proven #maths #mathematics and, since they are still undergrads, #citizenscientist

Since the Babylonians, we all knew that the basis of trigonometry can’t be proven. It must be assumed. Until today, when a new proof has been presented!

Pythagoras’s theorem, a2+b2=c2, which says that the square of the hypotenuse is equal to the sum of the squares of the opposite two sides of a right triangle. It’s the basis of trigonometry, so mathematicians have long held that any trigonometric proof of the theorem would be fallacious: circular reasoning. That’s because you can’t validate an idea with the idea itself. Craig Good – sign up for Skeptoid’s Wonder of the Week

Well! At the American Mathematical Society’s March meeting (okay, it wasn’t today, but I’m just catching up) two undergraduates challenge that venerable notion.

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. 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. Session abstract

As an engineer, I am only an egg when it comes to math. I stand in awe of such an accomplishment, and am happy to share my humble amazement. Perhaps a mathematician or member of the AMS can offer more intelligent comments below this post. Will this proof withstand scrutiny?

Congratulations to Ne’Kiya D Jackson and Calcea Rujean Johnson of St. Mary’s Academy, New Orleans, LA