'Impossible' Proof of Pythagorean Theorem by Two High School Seniors

Nothing MAGA-related here except for the cartoon

Here's an inspiring story I ran across on Live Science that I thought would be worth sharing, particularly for the math afficionados among us, and anyone who appreciated the movie Hidden Figures.

Most of us have probably at least heard of the Pythagorean Theorem that states that the sum of the squares of the two shorter sides in a right triangle are equal to the square of its longest side, the hypotenuse -- which is one of the foundations of both Geometry and Trigonometry.

What's practically unheard of is actually trying to prove the theorem (in the mathematical sense) using  only trigonometry without resorting to any sort of circular reasoning, but that's precisely what these two remarkable young Black women, Ne'Kiya Jackson and Calcea Johnson, managed to do a couple of years ago when they were both high school seniors in Louisiana:

Jackson and Johnson came up with their "impossible" proof in answer to a bonus question in a school math contest. They presented their work at an American Mathematical Society meeting in 2023, but the proof hadn't been thoroughly scrutinized at that point. Now, a new paper published Monday (Oct. 28) in the journal American Mathematical Monthly shows their solution held up to peer review. Not only that, but the two students also outlined nine more proofs to the Pythagorean theorem using trigonometry.

"To have a paper published at such a young age — it's really mind-blowing," Johnson, who is now studying environmental engineering at Louisiana State University, said in a statement emailed to Live Science. "I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things."

Note:  edited to clarify an important missing concept (i.e. their proof was based solely on trigonometric equations that did not themselves rely on the Pythagorean Theorem in any way).