Teens Say They Have New Proof for 2,000-Year-Old Mathematical Theorem, a Method Scholars Thought Impossible
Two New Orleans high school students claim to have solved a 2,000-year-old puzzle in mathematics, which scientists are saying should be submitted to peer review.
Calcea Johnson and Ne’Kiya Jackson from St. Mary’s Academy presented their findings to a meeting of the American Mathematics Society in which they explain they were able to prove Pythagoras’ Theorem using trigonometry rather than circular logic.
For the mercifully uninitiated, trigonometry is the study of triangles. Pythagoras’ Theorem deals with triangles that are not perfectly symmetrical, and it goes like this.
The area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. It is written as a2+b2=c2.
One of the interesting things about this equation is that for 2,000 years, no mathematician has been able to demonstrate the truth of it without simply using the equation itself as proof; what is called circular logic, and not accepted as truth evidence of proof.
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Johnson and Jackson reference Elisha Loomis’s The Pythagorean Proposition, a book investigating this concept, which “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 girls wrote.
It was this conundrum that they managed to untangle, presenting “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,” they said in their abstract. The equation they cite for this is sin2x+cos2x=1.
While we let mathematicians work out whatever that means, Catherine Roberts, executive director for the American Mathematical Society, encouraged the young ladies to submit their work for peer review, and commit themselves further to the study of mathematics so they can further advance the mathematical literature.
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The two ladies were interviewed on WWL New Orleans, and said it was an “unparalleled feeling” to present their findings to the society.
“There’s nothing like it—being able to do something that people don’t think that young people can do,” Johnson said to the station. “You don’t see kids like us doing this—it’s usually, like, you have to be an adult to do this.”
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