Summary: Two teenage mathematicians who independently discovered new ways to prove Pythagoras’ theorem have published their groundbreaking findings in a peer-reviewed journal. Calcea Johnson and Ne’Kiya Jackson present five new trigonometric proofs of the famous theorem, along with a method for finding five additional proofs, challenging long-held assumptions about mathematical proof methods.
Journal: American Mathematical Monthly, October 28, 2024, DOI: 10.1080/00029890.2024.2370240
Reading time: 4 minutes
Breaking Mathematical Barriers
In 2022, two high school students accomplished what many thought impossible: proving Pythagoras’ theorem using trigonometry. The feat, achieved by Calcea Johnson and Ne’Kiya Jackson, has now been documented in their first peer-reviewed paper published in the American Mathematical Monthly.
The significance of their achievement extends beyond the mathematical community. The discovery earned them keys to the city of New Orleans and recognition from Michelle Obama.
A Fresh Perspective on Ancient Mathematics
The 2,000-year-old Pythagorean theorem (a² + b² = c²) has been proven many times using algebra and geometry. However, proving it with trigonometry was considered impossible because trigonometry’s fundamental formulas assume the theorem is true—creating a circular reasoning problem.
“I was pretty surprised to be published,” says Ne’Kiya Jackson. “I didn’t think it would go this far.”
“To have a paper published at such a young age — it’s really mind blowing,” agrees Calcea Johnson.
Clarifying Mathematical Confusion
The researchers identified a key insight about trigonometry education: two different versions of trigonometry exist using the same terms, creating confusion for students. They compare this to trying to understand a picture with two different images printed on top of each other.
By separating these versions and focusing on just one, they discovered multiple new ways to prove the famous theorem. Their paper presents five new proofs and a method for finding five more, with nine of these proofs being completely new to the mathematical community.
Inspiring the Next Generation
Currently, Jackson studies pharmacy at Xavier University of Louisiana, while Johnson pursues environmental engineering at Louisiana State University’s Roger Hadfield Ogden Honors College. Their achievement carries special significance for representation in STEM fields.
“I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things, and to let other young women know that they are able to do whatever they want to do,” says Johnson.
The significance of their work has been recognized by the mathematical community.
“The Monthly is honored and delighted to publish the work of these two students on its pages,” says Della Dumbaugh, editor-in-chief of American Mathematical Monthly. “Their results call attention to the promise of the fresh perspective of students on the field. They also highlight the important role of teachers and schools in advancing the next generation of mathematicians.”
Further Reading:
– Original Research Paper
– American Mathematical Society Conference Proceedings
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