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Students may have come up with an “impossible” proof of the Pythagorean Theorem | Sciences

Two high school students in the United States may have proven the Pythagorean theorem using trigonometry, something mathematicians consider impossible. Article written by Calcee Johnson and Nikia Jackson, St. Mary’s Academy in New Orleans has not yet been validated by her peers, but she has impressed industry professionals.

On March 18, they presented their findings at a sectional meeting of the American Mathematical Society (AMS). “It’s an incomparable feeling, frankly, because there’s nothing quite like it — being able to do something that people don’t think young people can do,” Johnson said. to New Orleans television news station WWL.

The Pythagorean theorem dates back 2,000 years and states that the sum of the squares of two shorter sides of a right-angled triangle is equal to the square of the hypotenuse. It is the basis of trigonometry, which comes from the Greek words for triangle (Trigonon) and measure (Metron).

The Pythagorean theorem states that the sum of the squares of two shorter sides of a right triangle is equal to the square of the hypotenuse – Image: Wikimedia Commons

This area of ​​mathematics determines how the lengths of the sides and angles of a triangle are related. so why, According to the portal Science livesMathematicians have always believed that using trigonometry to prove a theorem would constitute a flaw in logic known as circular reasoning.

In the Summary of your articleJohnson and Jackson cited the book Pythagoras proposalby American mathematician Elisha Loomis (1852-1940). In the work he says that “there are no trigonometric proofs, because all the basic formulas of trigonometry are based on the truth of the Pythagorean theorem.”

But for a student duo, that’s not true. “In our talk, we present new evidence for the Pythagorean theorem that is based on a fundamental result of trigonometry—the law of sine—and show that the proof is independent of the Pythagorean trigonometric identity \sin^2x + \cos^2x=1,” they write in the article summary.

“It is very unusual for high school students to attend an AMS sectional meeting,” said Scott Turner, director of communications for AMS. Science lives. “After the presentation at the conference, the next step will be to submit their work to a peer-reviewed journal where members of our community can examine their findings to determine whether their evidence is a valid contribution to the mathematical literature,” explained Katherine Roberts. Executive Director of the AMS Portal.

Therefore, it is still too early to say whether Calcea and Ne’Kiya will revolutionize this scientific field, but they certainly have a promising future ahead of them.

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