Two teenagers made significant strides in Mathematics after proving the Pythagorean Theorem with trigonometry.
Even better, the US youths provided nine solutions after presenting their previous one, blowing away the math community.
However, the science news website Popular Mechanics reported that the wunderkind pair hadn’t submitted their work to a peer-reviewed publication at the time of writing.
How did the teens solve the Pythagorean Theorem?
In December 2022, a high school teacher at St. Mary’s Academy in New Orleans asked students to prove the Pythagorean Theorem with trigonometry.
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Science news platform Interesting Engineering reported she offered a $500 reward, but she likely did not expect a compelling solution.
Nevertheless, Calcea Johnson and N’Kiya Jackson took the challenge. Popular Mechanics said they used the Law of Sines while avoiding the Pythagorean theorem’s trigonometric identity (sin²α + cos²α = 1).
In 1968, American mathematician Elisha Loomis said the challenge was impossible, stating:
“There are no trigonometric proofs because all of the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.”
The Pythagorean Theorem is (a2 + b2 = c2), which states that the sum of the two shortest sides of a right triangle is equal to that triangle’s longest side.
On the other hand, trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of a triangle.
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That is why many mathematicians resort to circular reasoning when trying to prove the theorem. In other words, they prove PT by using the theorem itself.
Jackson and Johnson disproved this notion despite the odds and defied the impossible. They told local news station WWL:
“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.”
“A lot of times you see this stuff, you don’t see kids like us doing it.”