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# US Students Prove Pythagorean Theorem In “Impossible” Way Calcea Johnson and Ne’Kiya Jackson have proven the famous theorem of the great ancient Greek mathematician Pythagoras in an “impossible” way. Credit: Facebook / St Mary’s Academy, New Orleans

Two American high-school students claim they have proven the most famous theorem of great ancient Greek mathematician Pythagoras in a way that has been previously thought “impossible” by scholars.

According to their school, St. Mary’s Academy in New Orleans, US, Calcea Johnson and Ne’Kiya Jackson have successfully used trigonometry without circular logic to prove the 2000-year-old Pythagorean Theorem – a fundamental relation of geometry.

The 17-year-old girls, who became interested in the Pythagorean Theorem by entering a math contest at St. Mary’s Academy, presented their research in Atlanta, Georgia at Georgia Tech on Saturday, March 18, 2023.

“Their groundbreaking lecture from the research is historic. High School students are generally not presenters at the American Mathematical Society Meeting,” the school’s announcement notes.

### 17-year-old students prove scholars wrong

In the 2000 years since trigonometry was discovered, it’s always been assumed that any alleged proof of Pythagoras’ Theorem based on trigonometry must be circular.
“In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “there are no trigonometric
proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem,” the St Mary’s Academy explains in a Facebook post.
However, the unprecedented research conducted by Calcea Johnson and Ne’Kiya Jackson concluded that this isn’t quite true.
“Their new proof of Pythagoras’s Theorem, which is based on a fundamental result in trigonometry —the Law of Sines— shows that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1.
“That all proves that Pythagorean Theorem based on trigonometry can indeed not consist of circular trigonometry,” it adds.

### Pythagorean is the most majestic theorem of mathematical science

Pythagoras and his school played a most crucial role in the history of mathematics.

Other than his famous theorem, the ancient Greek mathematician and philosopher was credited with many scientific discoveries, including Pythagorean tuning, the five regular solids, the Theory of Proportions.

But the Pythagorean Theorem is widely considered as the relation that changed the history of mathematics; geometry, trigonometry, algebra, differential equations and even imaginary complex numbers were founded using it as their basis.

Although the relation described by the popular theorem was probably known to mathematicians in Babylon, China, Mesopotamia, and India to be valid long before Pythagoras, it had been only acknowledged as an empirical, unproven observation.

Pythagoras was the first person to prove it, hence the theorem was named after him.

It was later proven by many mathematicians, both geometrically and algebraically.

Besides mathematics, Pythagoras made developments regarding the spherical nature of the Earth, and he is thought to have been the first scholar to divide the globe into five climatic zones.

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