Ne’Kiya Jackson and Calcea Johnson, in their final year at St. Mary’s Catholic High School in New Orleans—a school established after the U.S. Civil War to teach African-American girls—discovered a new way to prove the Pythagorean Theorem using trigonometry. For 2,000 years, mathematicians have said that it would be impossible to use trigonometry to prove the theorem, since it would depend upon a partial use of the theorem itself, which would be “circular reasoning.”
The girls, however, thought “outside the box”—or in this case, quite literally, outside the triangle. Upon their right triangle, they constructed a clever series of triangles, progressively smaller in size. They called the construction a “waffle cone.” Then they developed a formula for the geometric series of shrinking triangles inside their waffle cone. There was a lot of trial and error involved, they said, but they were able to duplicate the results of the original theorem. More details on their math can be seen here.
Since their initial discovery, they have discovered several other proofs to the same problem. They are still waiting for a mathematical journal to publish their results, but many mathematicians have already reviewed their work and have confirmed their results. New Orleans gave them “the key” to the city. Pythagoras, who ran his own city, would be proud.
