According to the Guardian, two American high school students have astounded mathematicians by claiming to have found a new way to use trigonometry to demonstrate Pythagoras’ theorem, a feat that was previously regarded to be impractical.
Seniors at St. Mary’s Academy in New Orleans, Calcea Johnson and Ne’Kiya Jackson presented their research on March 18 at the American Mathematical Society’s (AMS) Spring Southeastern Sectional Meeting.
”Their groundbreaking lecture from the research is historic. High School students are generally not presenters at the American Mathematical Society Meeting,” the school’s announcement notes.
Notably, the 2,000-year-old Pythagorean theorem asserts that the square of the hypotenuse, the third side opposite the right angle, is equal to the sum of the squares of the two shorter sides of a right triangle. Students from all over the world acquired the notation that reads a2+b2=c2 to express the theory.
However, mathematicians have been unable to come up with a conclusive proof for the theorem that would not only demonstrate its correctness but also illuminate its logic.
‘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,” they told an audience at the American Mathematical Society Southeastern Regional Conference.
The students established Pythagoras’ theorem without using circular reasoning by utilizing trigonometry
”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.”
The students added that they could establish the theorem without using circular reasoning by utilizing trigonometry.
But “that isn’t quite true,” the teenagers wrote in the abstract. “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 sin2x+cos2x=1.”
However, a peer-reviewed journal has not yet accepted the findings. It’s still too early to determine whether their evidence will ultimately hold up, according to Live Science.