Two young Louisiana students have made an incredible discovery by using only trigonometry to prove Pythagoras’ theorem, something many believed was impossible. Their findings have caused a stir in the mathematical community and generated fresh debates over basic geometric concepts.
Pythagoras’ theorem, which states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two shorter sides, has been a fundamental principle of mathematics for more than 2,000 years. Since trigonometry is based on the theorem itself, it was generally accepted that a purely trigonometric demonstration was impossible despite hundreds of proofs, which led to a circular debate. These high school pupils, however, were unwilling to accept this restriction.
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Ne’Kiya Jackson and Calcea Johnson, who were students in Louisiana at the time, embarked on a bold quest in 2022, to demonstrate Pythagoras’ theorem in a manner never seen before. They presented their ground-breaking evidence at the annual meeting of the Mathematical Association of America in Atlanta in March 2023, following four years of investigation and improvement.
The approach they employ is a trigonometric proof that eliminates any reliance on Pythagoras’ theorem itself by avoiding the conventional sine and cosine foundations. To overcome the purported dilemma, they instead turned to proportional reasoning and basic angle principles.
The mathematics community’s response was nothing short of spectacular. Experts who had previously ruled out the possibility of such proof were compelled to reconsider. In addition to receiving accolades at the conference, their work was expedited for publication in the esteemed American Mathematical Monthly.
Their proof not only resolved the issue but also paved the way for more. The adaptability of their method was demonstrated by the students’ introduction of other approaches, one of which produced five additional proofs.
According to mathematician Tom Murdoch, their work is revolutionary and has the potential to stimulate fresh thinking in geometry, trigonometry, and other fields.
Despite their success in the field of mathematics, Ne’Kiya Jackson and Calcea Johnson are still focused on their future professional endeavors.
