The ‘Impossible’ Puzzle Has Been Solved

[Gaffurio_Pythagoras.png: Franchino Gaffurio (publisher)derivative work: Singinglemon, Public domain, via Wikimedia Commons]

Two remarkable teenagers in New Orleans have done the impossible. They have solved an ancient puzzle that has stumped some of the most brilliant mathematicians throughout history. 

Local CBS writes, “Calcea Johnson and Ne’Kiya Jackson just gave a presentation to the American Mathematical Society’s Annual Southeastern Conference. They say they’ve proved Pythagoras’ Theorem can be proven without trigonometry — something that many thought was impossible.

‘It’s really an unparalleled feeling, honestly, because there’s just nothing like being able to do something that people don’t think young people can do,’ Calcea said. “A lot of times you see this stuff, you don’t see kids like us doing it.

If you need a refresher on Pythagorean Theory, you’re not alone.

Calcea and Ne’Kiya explained it to me like this: Basically, trigonometry is based on Pythagoras’ Theorem (A^2 + B^2 = C^2, sound familiar?), so using trigonometry to prove Pythagoras’s Theorem is what’s known as circular logic.”

The Pythagorean Proposition by Elisha Loomis, which contains the largest known collection of theorem proofs, ‘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,’ according to Johnson and Jackson’s abstract,” First Post noted.

“That isn’t quite true, the idea responds. ‘We present a new proof of Pythagoras’ Theorem based on a fundamental trigonometric result – the Law of Sines – and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1,” the pair claims.”

What the girls did, however, was show a way to prove the legendary theorem without using circular logic, “something mathematicians have been trying to do for nearly 2,000 years.”

“Alluding to how St Mary’s slogan is ‘No excellence without hard labor,’ the two students credited their teachers at the all-girls school in New Orleans’s Plum Orchard neighborhood for challenging them to accomplish something which mathematicians thought was not possible.

‘We have really great teachers,’ Jackson said to WWL during an interview published Thursday.

WWL reported that Jackson and Johnson are on pace to graduate this spring, and they intend to pursue careers in environmental engineering as well as biochemistry,” wrote The Guardian.

We can’t wait to see what they do next. 

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