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Two Black girls have discovered new proof for a 2,000-year-old mathematical theorem


This is the epitome of Black Girl Magic.


Two New Orleans high school seniors who claim they have proven Pythagores's theorem by using trigonometry - a feat academics have considered impossible for two millennia - have been invited by an influential US mathematical research organization to publish their work in a peer-reviewed journal.


St Mary's Academy students Calcea Johnson and Ne'Kiya Jackson recently presented their findings at the American Mathematical Society's southern chapter's semi-annual meeting in Georgia.

They were the only two high schoolers invited to give presentations at the meeting attended by math researchers from various institutions in Alabama, Georgia, Louisiana State, Ohio State, Oklahoma, and Texas. During their presentation, they discussed how they discovered a new proof for the Pythagorean theorem.


The 2,000-year-old theorem established that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse – the third, longest side opposite the shape’s right angle. The notation that summarizes the theorem has been taught to thousands of schoolchildren: a2 + b2 = c2.


In Johnson and Jackson's abstract for their presentation at the 18 March mathematical society, they mention how the theorem supports trigonometry.

According to Johnson and Jackson, the book with the greatest collection of proofs for the Pythagorean theorem – Elisha Loomis’s The Pythagorean Proposition – “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’.”


But, the two young mathematicians assert their counterpoint: “We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry – the Law of Sines – and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.” In short, they could prove the Pythagorean theorem using trigonometry, a feat that mathematicians for the past 2,000 years have maintained was only possible by circular reasoning, a logical fallacy in which someone tries to prove an idea with the idea itself.

According to Johnson, it was an “unparalleled feeling” sharing her and Jackson's research alongside researchers from universities.


“There’s nothing like it – being able to do something that people don’t think that young people can do,” Johnson said to the station. “You don’t see kids like us doing this – it’s usually, like, you have to be an adult to do this.”

Congratulations to Calcea Johnson and Ne'Kiya Jackson for working out a 2,000-year-old problem, and quite literally making history! #BlackExcellence #BlackGirlMagic

Source: The Guardian

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