In this blog post, I will introduce you to two amazing high school seniors from New Orleans, Calcea Johnson and Ne’Kiya Jackson, who have made a historic mathematics discovery. They have found a new way to prove the Pythagorean theorem using trigonometry, which is something that many mathematicians thought was impossible. I will tell you more about their backgrounds, their interests, their motivations and their achievements.
Who are Calcea Johnson and Ne’Kiya Jackson?
Calcea Johnson and Ne’Kiya Jackson are students at St. Mary’s Academy, a Catholic all-girls school in New Orleans. They are both 18 years old and plan to pursue careers in STEM fields.
Calcea Johnson is passionate about mathematics and physics. She loves to solve challenging problems and learn new concepts. She is also interested in music and plays the piano and the violin. She hopes to study engineering at MIT or Stanford.
Ne’Kiya Jackson is fascinated by biology and chemistry. She enjoys conducting experiments and exploring the natural world. She is also a talented writer and poet. She wants to study medicine at Harvard or Yale.
How did they become interested in the Pythagorean theorem?
The Pythagorean theorem is one of the first topics that they learned in their geometry class. They were intrigued by the simplicity and beauty of this theorem, which relates the lengths of the sides of a right-angled triangle. They wanted to know more about its history, its applications and its proofs.
They decided to do some research on their own and found out that there are hundreds of different ways to prove the Pythagorean theorem, some using algebra, geometry, calculus or even physics. They also learned that there is a book called The Pythagorean Proposition by Elisha Loomis, which contains 367 proofs of this theorem.
They were surprised to discover that none of these proofs used trigonometry, which is another branch of mathematics that deals with the study of triangles. They wondered why this was the case and decided to investigate further.
What did they discover and how did they prove it?
They discovered that there is a common belief among mathematicians that there are no trigonometric proofs of the Pythagorean theorem. The reason for this belief is that trigonometry depends on the Pythagorean theorem, so any attempt to prove it using trigonometry would involve circular reasoning, which is a logical fallacy.
However, they were not convinced by this argument and decided to challenge it. They found a way to use the law of sines, which is a fundamental result in trigonometry, to prove the Pythagorean theorem without using circular reasoning. Their proof is elegant, original and independent of the Pythagorean theorem.
They presented their proof at the American Mathematical Society’s south-eastern chapter’s semi-annual meeting in Georgia in March 2023. They were reportedly the only two high schoolers to give presentations at the meeting attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech.
Why is their discovery important and what are the implications?
Their discovery is important because it shows that there is more than one way to approach a mathematical problem. It demonstrates that even a well-known and ancient result like the Pythagorean theorem can still be explored and discovered from different perspectives. It also challenges the conventional wisdom that there are no trigonometric proofs of the Pythagorean theorem.
Their discovery has implications for both mathematics education and research. It can inspire students and teachers to learn more about geometry and trigonometry, and to look for new connections and insights. It can also motivate researchers to revisit old problems and find new solutions or generalizations.
In conclusion, Calcea Johnson and Ne’Kiya Jackson are two remarkable young women who have made a historic mathematics discovery. They have found a new way to prove the Pythagorean theorem using trigonometry. Their discovery is remarkable, elegant and original. It is a testament to their creativity, curiosity and perseverance. They have contributed to the advancement of mathematics and deserve recognition and praise for their achievement.