Teens Prove Pythagorean Theorem Using Trigonometry, Defying Centuries of Mathematical Dogma
In a historic mathematical achievement, two high school students, Calcea Johnson and Ne’Kiya Jackson, have challenged a centuries-old belief that it’s impossible to prove the Pythagorean Theorem using trigonometry. Their success has sparked global admiration while reigniting conversations about diversity in STEM and how education can transform lives.
A Historical Context: The Pythagorean Theorem Conundrum
The Pythagorean Theorem is perhaps the most iconic concept in geometry: a² + b² = c². For over 2,000 years, mathematicians believed that proving the theorem using trigonometry was impossible due to a logical fallacy known as circular reasoning. However, Johnson and Jackson took on this daunting task and presented their proof at an American Mathematical Society conference in March 2023.
Their work represents not only a milestone for mathematical achievements but also a triumph for representation in STEM fields. With young Black women historically underrepresented in the field, this discovery carries broader implications.
The “Impossible” Bonus Question: A Quest Begins
In December 2022, a school-wide math contest at their high school, St. Mary's Academy, motivated Johnson and Jackson to solve the seemingly impossible problem. The bonus question was to come up with a new proof of the Pythagorean Theorem using trigonometry. Despite being told that such a proof was unattainable, they dove headfirst into the problem.
“I was motivated because there was a monetary incentive,” Ne’Kiya Jackson explained, referring to the $500 prize. “500 dollars is a lot of money,” Calcea Johnson added.
Over the next two months, they worked tirelessly in pursuit of a solution. They wrote pages of calculations, filled their trash bins with crumpled sheets of equations, and encountered frustration at every wrong turn. “I started something, I need to finish it,” Johnson said.
Their perseverance paid off. The solution they presented at the American Mathematical Society conference was nothing short of revolutionary.
A Groundbreaking Proof: The Waffle Cone and Circle Triangle
Their innovative proofs, known as the Waffle Cone and Circle Triangle methods, drew on trigonometric principles to build a series of infinitely decreasing similar triangles.
Waffle Cone Proof: Johnson’s proof begins by creating a waffle cone-like pattern with right triangles inside a larger right triangle. The pattern involves drawing congruent triangles and extending lines until they meet, ultimately forming a cone. The law of sines is then used to demonstrate the theorem.
Circle Triangle Proof: Jackson’s proof involves a right triangle inside a circle and a perpendicular bisector that divides the original triangle into two smaller triangles. These smaller triangles are then used to prove the theorem.
Initial Reaction and Media Buzz
Their teachers submitted the proofs to the American Mathematical Society, and the duo presented them in March 2023. Once word spread, their achievement quickly went viral.
“It blew up,” Johnson noted, describing how media outlets from South Korea to the United States praised their work. Former First Lady Michelle Obama offered congratulations, and they received keys to the city of New Orleans and commendations from Louisiana's governor.
“I just love this story. Way to go, Ne’Kiya and Calcea!” wrote Michelle Obama.
Challenges and Skepticism
While their achievement was widely celebrated, skepticism emerged in some corners of the mathematical community. Some individuals criticized the notion that their proof was “unprecedented,” given that mathematician Jason Zimba presented a trigonometric proof in 2009.
However, many mathematicians praised the duo's originality and confirmed their solution’s validity. “The proof is original, elegant, and undoubtedly correct,” stated one analyst.
Charles Murray, an author and commentator known for controversial views on race and intelligence, doubted their ability to solve the theorem, assuming their proof would be discredited. However, Johnson and Jackson remained unfazed and focused on their education.
The Journey Beyond High School
After graduating from St. Mary’s Academy, Johnson and Jackson moved on to pursue higher education. Johnson, the valedictorian, chose environmental engineering at Louisiana State University, while Jackson opted for pharmacy at Xavier University. Despite their mathematical brilliance, both were reluctant to pursue careers in the field.
“People might expect too much out of me if I become a mathematician,” Jackson joked, while Johnson added, “I may take up a minor in math, but I don’t want that to be my job job.”
St. Mary's Academy: A Culture of Achievement
St. Mary’s Academy, a Catholic school in New Orleans founded to educate Black girls after the Civil War, played a pivotal role in their success. The school's principal and interim president, Pamela Rogers, emphasized the unwavering belief in every student’s potential.
“We believe all students can succeed, all students can learn,” Rogers said. “It does not matter the environment that you live in.”
Gloria Ladson-Billings, a professor emeritus at the University of Wisconsin, pointed to the importance of expectations. “When teachers lay out some expectations that say, ‘You can do this,’ kids will work as hard as they can to do it,” she noted.
The Future of STEM Diversity and Excellence
The success of Johnson and Jackson serves as a beacon of inspiration, not only for young Black women but for anyone interested in pursuing STEM. It highlights the importance of nurturing environments like St. Mary’s Academy, where students are encouraged to push boundaries and redefine possibilities.
Their story also underscores the importance of breaking stereotypes and recognizing excellence, no matter the form it takes. For years, many people underestimated the potential of Black women in mathematics. Johnson and Jackson's achievement serves as a powerful rebuttal to such misconceptions.
As they continue their academic journeys, the future of mathematics remains bright, and their work will undoubtedly inspire future generations to challenge longstanding assumptions and strive for greatness.
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