US teens find new way to prove Pythagoras's theorem, mathematicians thought it impossible
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New Orleans: Two high school students from the US have proved Pythagoras' theorem by using trigonometry. Mathematicians have previously thought it impossible.
The Pythagorean theorem is 2000 years old and states 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.
Students learn it by using the equation a2+b2=c2.
Mathematicians have struggled to find definitive proof for the famous theorem. Such proof is supposed to show the theorem works and explain why it works.
The school, St. Mary's Academy in New Orleans, in announcement notes said that the students' groundbreaking lecture from the research is historic. "High School students are generally not presenters at the American Mathematical Society Meeting." Calcea Johnson and Ne'Kiya Jackson presented their findings at the American Mathematical Society's (AMS) Spring Southeastern Sectional Meeting on March 18.
"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," said the students.
They added that they can not only prove the theorem by using trigonometry but also without using 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 new proof is not yet accepted into a peer-reviewed journal and it is too soon to say whether it will be.
