Mathematicians have believed for almost two thousand years that it was impossible to prove the Pythagorean theorem using trigonometry, but now two students claim to have done it.
Two students from St Mary’s Academy, a high school in New Orleans (USA), presented last week before the American Mathematical Society. a New way to prove the Pythagorean theorem. They did it using trigonometry, a branch of mathematics that is more than two thousand years old with which it was previously believed impossible to confirm this principle of geometry.
Calcea Johnson and Ne’Kiya Jackson claim that they managed to find a new proof of the Pythagorean theorem that is based on trigonometry. the young used the law of sinesbased on trigonometry, to show that the sum of the squares of the legs of a triangle is equal to the square of the hypotenuse.
“We present a new proof of the Pythagorean theorem that is based on a fundamental result of trigonometry: the Law of Sines, and we show that the proof is independent of the Pythagorean trigonometric identity sin2x+cos2x=1,” the girls argued.
The two students referred in their study to the book ‘The Pythagorean Proposition’, written by Elisha Loomis, which contains the largest number of proofs of the theorem, stating that the statement that “there are no trigonometric proofs because all the fundamental formulas of trigonometry are based on the truth of the Pythagorean theorem“, described there, was not true. Johnson and Jackson noted that they were able to prove the theorem by avoiding that circular logica term used when someone tries to validate an idea with the idea itself.
“It’s really an incomparable feelinghonestly, because there’s nothing like being able to do something that people don’t think young people can do,” Johnson said. The girls said their discovery was made possible by the work of their teachers.
Source: RT
