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.

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. Allegedly, they were the exclusive pair of high school students delivering presentations at the gathering, which drew mathematicians from various institutions such as 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.

Conclusion

In conclusion, Calcea Johnson and Ne’Kiya Jackson are two remarkable young women who have made a historic mathematics discovery. They’ve discovered an innovative approach to demonstrating the Pythagorean theorem by employing 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.

Thomas Amoani is a young and brilliant African student who has made headlines for his academic achievements in economics. He recently emerged as the best student in the Department of Economics and Business Finance at Brunel University London, United Kingdom. This is not the first time that Amoani has impressed the world with his excellence. In 2020, he aced the West African Examination Council (WAEC) examination by scoring A’s in all the eight subjects he registered. His remarkable accomplishment secured him a scholarship from President Akufo-Addo of Ghana to pursue studies in Economics and Business Finance at Brunel University London.

Amoani hails from Ghana, West Africa, where he attended the Presbyterian Senior High School, Adeiso. He was among the first batch of students who benefited from the Free Senior High School policy introduced by the Ghanaian government in 2017. The policy aims to provide access to quality education for all Ghanaian students regardless of their financial background. Amoani took advantage of this opportunity and worked hard to achieve his academic goals.

At Brunel University London, Amoani continued to showcase his brilliance and enthusiasm for economics. He was photographed crossing the stage at the esteemed university to accept the award for the Overall Best Economics Student. He also received a certificate of excellence from the university for his outstanding performance. Amoani has expressed his gratitude to God, his family, his teachers, and his mentors for their support and guidance throughout his educational journey.