Two students who discovered a seemingly impossible proof to the Pythagorean theorem in 2022 have wowed the math community again with nine completely new solutions to the problem.
While still in high school, Ne'Kiya Jackson and Calcea Johnson from Louisiana used trigonometry to prove the 2,000-year-old Pythagorean theorem, which states that the sum of the squares of a right triangle's two shorter sides are equal to the square of the triangle's longest side (the hypotenuse). Mathematicians had long thought that using trigonometry to prove the theorem was unworkable, given that the fundamental formulas for trigonometry are based on the assumption that the theorem is true.
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 Monthlyshows 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.
It’ll sound like splitting hairs, but I’ll try:
Trigonometry is based on the Pythagorean theory being true. They proved the Pythagorean theorem effectively in reverse without using the theorem itself as a basis. So they used the structure of trigonometry to prove the basic underlying principle of trigonometry. Bad analogy: kind of like if you have an airplane first, and THEN you worked out the physics of lift. You knew it could fly and how to fly it, but never questioned how it worked.