Pythagorean Theorem: Calcea Johnson & Ne'Kiya Jackson Create Proof
Calcea Johnson and Ne’Kiya Jackson Create Proof For The Pythagorean Theorem
Calcea Johnson and Ne’Kiya Jackson, two Black seniors from St. Mary’s Academy in New Orleans, have done the unthinkable. In 2022, the amazing students created proof for the Pythagorean Theorem, which you may know as a² + b² = c², but their math journey is far from over.
This past spring, they submitted their high school proofs for meticulous peer review and prospective publication while continuing their exploration into further proofs of the Pythagorean Theorem, according to their new interview on 60 Minutes with Bill Whitaker, published May 6.
Reflecting on their progress, Johnson remarked, “We found five. And then we found a general format that could potentially produce at least five additional proofs.”
If you’re unfamiliar with the age-old math problem, picture a triangle with a right angle, like the corner of a square. The Pythagorean Theorem tells us that if you take the lengths of the two shorter sides, square each of them (multiply them by themselves), and then add those results together, you’ll receive the length for the third side.
Johnson and Jackson courageously took on the challenging geometry equation and were assigned the formidable task of devising a proof for the math conundrum. The endeavor was part of a school-wide math contest held in December 2022, offering a tempting cash prize of $500.
The dedicated students were well-versed in geometry and even dabbled in trigonometry, yet both agreed that math wasn’t a walk in the park. Little did they know, there existed over 300 recorded proofs of the Pythagorean Theorem, blending algebra and geometry seamlessly. But for two millennia, a proof incorporating trigonometry was deemed unattainable—a challenge that now lay before them as an unexpected bonus question.
Jackson told Whitaker she was motivated to solve the tough equation “because there was a monetary incentive.”
Johnson added, “$500 is a lot of money. So I– I would like to at least try.”
The incredible students worked for two months to create their proof.
After dedicating two months of diligent study, the students of St. Mary’s Academy successfully crafted a proof for the equation. Ultimately, it was Johnson and Jackson who cracked the problem, with Johnson affectionately naming their proof the Waffle Cone.
“So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta,” Johnson told Whitaker, attempting to explain the process that she and Jackson used to solve the equation.
“Then what we do next is we draw a second congruent, which means they’re equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually, it creates this larger waffle cone shape.”
Attempting to explain the concept further to a confused-looking Whitaker, Jackson added, “So you have a right triangle, 90° angle, alpha and beta. I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that’s basically what I used for the proof. That’s the proof.”
To check their work, Johnson, Jackson and St. Mary’s Academy math teachers presented their proof at an American Mathematical Society conference held in Atlanta in March 2023, where it was deemed accurate. Before their breakthrough, only one documented proof incorporating trigonometry had been achieved, courtesy of mathematician Jason Zimba in 2009.
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