Calcea Johnson and Ne'Kiya Jackson, two college students, have developed innovative proofs for the Pythagorean Theorem using trigonometry, expanding on a 2,000-year-old mathematical challenge. Their work, which includes five distinct proofs and a method revealing five additional proofs, was published in the American Mathematical Monthly. This research originated from a high school math contest at St. Mary's Academy in New Orleans, where they aimed to create a new proof for the theorem. Their contributions build on previous work by mathematician Jason Zimba, who submitted a trigonometric proof in 2009.
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Calcea Johnson and Ne'Kiya Jackson, who surprised the math world when they produced innovative solutions to a 2,000-year-old puzzle, wowed the math world again when they presented several new ways of proving the Pythagorean Theorem via trigonometry.
The two, now college students, have come up with five ways of solving the problem using trigonometry along with a method that reveals five other proofs. One of their proofs was previously presented at a conference and their new solutions were published Monday in the journal American Mathematical Monthly.
They started studying the math problem as part of a high school math contest at New Orleans' St. Mary's Academy. One of their proofs was previously presented at a conference and their new solutions were published Monday in the journal American Mathematical Monthly.
Della Dumbaugh, editor-in-chief of American Mathematical Monthly, said Jackson and Johnson's work calls attention to the promise fresh perspectives can bring to the field.
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The St. Mary's math contest
The students started researching as part of a school-wide math contest with a challenging bonus question, which asked students to create a new proof for the Pythagorean Theorem, a fundamental principle of geometry, using trigonometry.
Many mathematicians over the years have proved the theorem using algebra and geometry. For thousands of years, a proof using trigonometry was thought to be impossible. Mathematician Jason Zimba submitted one in 2009 and now Johnson and Jackson have added to the canon.
They were seniors in high school during the math contest, motivated by the promise of $500 in prize money. Over several months, the students spent almost all their free time developing their ideas.
Math teachers at St. Mary's later submitted Johnson and Jackson's proofs to an American Mathematical Society conference in Atlanta in March 2023.