Two Young Black Girls Find Trigonometric Proof Of The Pythagorean Theorem

The fundamental principle of geometry was said to be impossible to prove using trigonometry, but these brilliant minds found a way.

Meet Calcea Johnson and Ne'Kiya Jackson. These two young Black students are mathematical prodigies who attended St. Mary’s Academy in New Orleans. They are history-making teens who solved and showed proof of the age-old math giant, the Pythagorean Theorem ( a² + b² = c²). Many high schoolers are familiar with this equation, but proving it?

Students at St. Mary’s were offered a challenge by their math teacher, Michelle Blouin Williams, to create a proof of the Pythagorean Theorem. And there was a cash incentive of $500 on the line. There have been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry. Still, for 2,000 years, proof using trigonometry was thought to be impossible, and that was the task at hand.

For two months, the girls hunkered down and put in work trying to solve the seemingly impossible. Even Mrs. Williams didn't think there was a solution. Mrs. Williams said, “I was just looking for some ingenuity, you know—”

And then, one day, they cracked the trigonometry code, and the girls called their solve the Waffle Cone. They explained in an interview with 60 Minutes:

Calcea Johnson: 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. So then what we do next is we draw a second congruent, which means they're equal in size. Then, we start creating similar but smaller right triangles that go in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta. Okay, 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.

Is anyone else still lost?

Two Black Female High School Seniors May Have Discovered a New Proof For 2,000-Year-Old Math Theorem

Well, just know that Johnson and Jackson have joined the most exclusive club in mathematics as they both independently came up with proof that only used trigonometry. This feat is said to have been documented once before by mathematician Jason Zimba in 2009 – one in 2,000 years. 

Even after all of that, both Jackson and Johnson don’t even believe their geniuses or think they’re necessarily “good at math.”

When asked if the girls were unicorns, or rather, special students with special abilities, Mrs. Williams said, “Oh, no, no. If they are unicorns, then every single lady who has matriculated through this school is a beautiful, Black unicorn.”

That’s the beauty of St. Mary’s–every single student is a brilliant star. While the school is proud of Johnson and Jackson, their accomplishment is par for the course in attending a school like this one.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She said, “Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, ‘I'm not going to be anything special.’ What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships subsidized by fundraising to defray the $8,000-a-year tuition. There’s no test to get in, but there is a standard of excellence to uphold.

The school boasts a 100% graduation rate. Last year, when Johnson and Jackson graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Cheers to both young ladies for showing what is possible when learning and growth are supported in high school.

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