Two U.S. teenagers have left mathematicians stunned after they have reportedly discovered an advanced way to prove Pythagorean Theorem by using trigonometry, an achievement geometricians initially believed was unimaginable.
The students, Calcea Johnson and Ne’Kiya Jackson, who are currently in their last year at St. Mary’s Academy in New Orleans, showcased their findings at the American Mathematical Society’s (AMS) Spring Southeastern Sectional Meeting in March.
”Their groundbreaking lecture from the research is historic. High School students are generally not presenters at the American Mathematical Society Meeting,” the school said in an announcement.
The 2,000-year-old Pythagorean theorem expresses that the sum of the squares of a right triangle’s two shorter sides is the same as the square of the hypotenuse, the third side opposite the right angle. Globally, mathematicians have learned that the notation states the theory as a2+b2=c2. But, researchers have been unable to identify the specific proof for the theorem.
”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,” the students told an audience at the American Mathematical Society Southeastern Regional Conference. ”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.”
Johnson and Jackson further stated they can prove the theorem by utilizing trigonometry and with no circular reasoning.
“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,” the teenagers wrote in their abstract.
While the findings would prove to be revolutionary in the field of mathematics, it has not been officially accepted into peer-reviewed journals. More findings would need to be conducted to satisfy the conditions they have found.
