Two New Orleans students who solved the Pythagorean theorem using trigonometry have had their discovery confirmed by the math community after their findings were published in the American Mathematical Monthly this week, solidifying their proofs.
And if solving Pythagoras’ theorem wasn’t challenging enough, the young women, now college freshmen, also discovered nine more solutions to the problem.
Ne’Kiya Jackson and Calcea Johnson, former St. Mary’s Academy students, presented their discovery to the American Mathematical Society in Atlanta back in March of 2023. This October, their solutions were peer-reviewed and thoroughly investigated to confirm what many in the math community never could have imagined — the theorem could be solved by using trigonometry.
Many papers submitted to the mathematics journal are often turned down. But after careful consideration and scrutiny, Jackson and Johnson’s paper was approved for publication.
Jackson and Johnson found the first proof to the equation during their senior year of high school while working tirelessly over their holiday break to solve a bonus question in a math contest.
Once deemed impossible, the two students overcame a failure of logic referred to as circular reasoning. But, in their new study, Johnson and Jackson went even further, providing nine other proofs, or solutions to the theorem.
Since the foundation of trigonometry relies on the fact that the Pythagorean Theorem is true, the mathematics community believed using trigonometry to prove the theorem would be unworkable. But it wasn’t.
The 2,000 year-old theorem states that the sum of the squares on the legs of a right triangle is equivalent to the square on the hypotenuse, or the longest side of a right triangle.
Using a trigonometry rule called the Law of Sines, the students showed that the “proof is independent of the Pythagorean trig identity sin2x + cos2x = 1.”
In their published paper, the duo stated there are two ways to demonstrate trigonometry and its functions, but they are typically combined into one.
The ratios – sine and cosine – are determined by the right angle of the triangle. According to the paper, they can be illustrated using the trigonometric technique or by using polynomials (algebraic expressions composed of several variables and coefficients) of complex numbers.
The students managed to evade circular reasoning – essentially using the theorem to prove itself.
A year later, the students are in their first year of college. Jackson attends Xavier University of Louisiana and is studying pharmacology, while Johnson studies environmental engineering at Louisiana State University.
Their findings are testament to the idea that dedication pays off.
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