In a groundbreaking academic accomplishment, two US college students have expanded the understanding of Pythagoras’ theorem by developing five new trigonometric proofs, a feat previously thought unattainable. Calcea Johnson and Ne’Kiya Jackson, who first gained attention as high school students, published their innovative findings in the prestigious American Mathematical Monthly. Their work not only revisits a theorem dating back over two millennia but challenges longstanding mathematical beliefs regarding the theorem’s proof methods.
Rethinking a Timeless Theorem
Pythagoras’ theorem, represented by the equation a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, describes the relationship between the sides of a right-angled triangle, stating that the square of the hypotenuse equals the sum of the squares of the other two sides. Historically, mathematicians have proved this theorem using geometry and algebra, with attempts to prove it through trigonometry typically dismissed as circular reasoning.
Johnson and Jackson’s methods tackle the problem head-on without circular logic—a method that professional mathematicians had previously overlooked. Their initial success with this theorem as high schoolers in 2022 surprised the academic community, setting the stage for their recent work.
Ten Proofs and Expanding Knowledge
The duo’s latest achievement adds five distinct trigonometric proofs to the Pythagorean theorem and, by extension, offers insights leading to an additional five proofs. In total, Johnson and Jackson have provided ten new approaches, a substantial increase in the theorem’s body of knowledge. “I was pretty surprised to be published. I didn’t think it would go this far,” Jackson shared in a statement, underscoring her amazement at the recognition their work has garnered.
Impact on STEM Education
Their work has already inspired interest in STEM (science, technology, engineering, and mathematics) fields. Jackson expressed her enthusiasm for changing perceptions about these disciplines, remarking, “It’s very exciting for me because I know when I was growing up, STEM wasn’t really a cool thing. So the fact that all these people actually are interested in STEM and mathematics really warms my heart and makes me really excited for how far STEM has come.”
American Mathematical Monthly editor Della Dumbaugh highlighted the journal’s pride in publishing such impactful research, attributing the refined presentation of their work to Editorial Board member Grant Cairns.
Diverse Academic Futures
Despite their remarkable mathematical talents, neither Johnson nor Jackson plans to pursue mathematics as a career. Jackson is currently studying pharmacy at Xavier University in New Orleans, while Johnson is focused on environmental engineering at Louisiana State University, showing the range of interests among today’s emerging scholars.
With their groundbreaking research, Johnson and Jackson have not only revitalized discussions on Pythagoras’ theorem but have also inspired a new generation to explore mathematics and STEM, proving that innovation knows no age or field limitations.
Sources By Agencies
