PYTHAGORAS THEOREM PROOFE USING TRIGNOMETRIC-TWO GIRLS.

The Pythagoras theorem; one of the most popular mathematical theories has been subjected to a revolutionary path as two American girls decided to have a second microscopic analysis of the theory’s proof. According to sources, their work challenged age-old assumptions about trigonometry and Pythagoras theorem. Being one of the oldest theories in the world of mathematics, it has seemed impossible to all learners and teachers of mathematics;  this age-old theory is now being given a second thought at the groundbreaking work of two teenagers from Louisiana.

By proving Pythagoras theorem using trigonometry: the two Louisianan teenagers have done what for centuries seemed impossible. Their work has sparked the interest and picked the attention of all who live in the world of mathematics staging critical discussion and analysis of the foundation of geometric principles.

The Pythagoras theory propounds that in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the longer side called hypotenuse. From the time of Euclid to modern algebraic approaches  Pythagoras has stood as a pillar theory in Mathematics as widely believed that a pure trigonometric proof is impossible.

WHY?

Trigonometry was built on the theory of Pythagoras and hence seemed impossible to proof the theory upon which it has been built.

Attempts to use SOHCAHTOA to proof the theory lead to a circular argument as the method in turn depends on what it aspires to proof. However two high school students disproof this limitation in a groundbreaking work.

Calcea Johnson and Ne’Kiya Jackson-the two teenagers from Louisiana

The Groundbreaking Proof  by Calcea Johnson and Ne’Kiya Jackson
Ne’Kiya Jackson and Calcea Johnson, who were students in Louisiana at the time, embarked on the path of finding trigonometric proof of the Pythagoras theorem in 2022. They presented their ground-breaking evidence at the annual conference of the Mathematical Association of America in Atlanta in March 2023, following four years of investigation and improvement.

METHOD USED BY THE TWO?
Calcea Johnson and Ne’Kiya Jackson used a trigonometric proof that eliminates any reliance on Pythagoras’ theorem itself by avoiding the conventional sine and cosine foundations. To avoid the predicted paradox by a mathematician in the late 1800s named Elias Loomis who was a Ph.D. student at Yale. He said it was impossible to make a proof of the Pythagorean theorem using Trigonometry because any proof of the Pythagorean theorem that used Trigonometry would be circular reasoning, they instead turned to proportional reasoning and basic angle principles.

REACTION OF ACADEMIC DISCOURSE COMMUNITIES OF MATHEMATICS.
The mathematics community’s response was nothing short of spectacular. Professionals who have previously ruled out the possibility of such proof

Their proof didn’t just solve the problem but also helped opened the floodgates new understanding of mathematical principles. The students introduced multiple approaches, including one that generates five additional proofs, proving their method’s accuracy.

Mathematician Tom Murdoch described their work as a game-changer, stating that it could inspire new perspectives in geometry, trigonometry, and beyond.https://mathworld.wolfram.com/SOHCAHTOA.html#:~:text=%22SOHCAHTOA%22%20is%20a%20helpful%20mnemonic,(1)