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Two high school seniors from New Orleans are making major waves in the world of academia after solving a mathematical equation involving the Pythagorean Theorem that has stumped mathematicians for the last 2,000 years.
Calcea Johnson and Ne’Kiya Jackson of St. Mary’s Academy found a way to solve the Pythagorean Theorem using trigonometry without circular logic, WWL-TV reported.
If that sounds like mumbo jumbo, then consider this: most high school students learn about the famous theorem, which asserts that A^2+B^2=C^2. Essentially, the age old rule claims that the sum of the squares of a right triangle’s two shorter sides equals the sum of the square of the hypotenuse.
Yet for the last 2,000 years, the most renowned mathematicians haven’t been able to prove the theory without using the theory itself–until now.
Johnson and Jackson presented their findings at the American Mathematical Society’s Annual Southeastern Conference on March 18 in Atlanta. Among math researchers from the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech, Johnson and Jackson were the only two teens in attendance.
“It’s really an unparalleled feeling, honestly, because there’s just nothing like being able to do something that people don’t think young people can do,” Calcea Johnson said. “A lot of times you see this stuff, you don’t see kids like us doing it.”
Pythagorean Theorem: Solving a 2,000-year-old mathematical mystery
According to their presentation, the young ladies noted that even the most notable mathematicians had thought that solving the Pythagorean Theorem without using circular logic was impossible.
“There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem,” author Elisha Loomis stated in her book, “The Pythagorean Proposition.”
Yet Johnson and Jackson knew that wasn’t true, and they proved it.
“In our lecture 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 \sin^2x + \cos^2x = 1,” they wrote.
Now, according to The Guardian, the New Orleans high school seniors are being encouraged to submit their work into a peer-reviewed journal. Catherine Roberts is executive director for the American Mathematical Society.
“Members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature,” Roberts said.
Ultimately, the young ladies say they owe much of their success to a school whose motto–“No Excellence Without Hard Labor”–encourages them to strive for the impossible.
“We have really great teachers,” Ne’Kiya Jackson said.
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