Two young women - HS students in New Orleans - say they've solved a 2,000 year old mathematical problem

It has been believed that the Pythagorean Theorem (remember? A squared + B squared = C squared) could not be solved using trigonometry. However... Be fun to see if this passes peer review. The article is from the Guardian (UK).

Two New Orleans high school seniors who say they have proven Pythagoras’s theorem by using trigonometry – which academics for two millennia have thought to be impossible – are being encouraged by a prominent US mathematical research organization to submit their work to a peer-reviewed journal.

Calcea Johnson and Ne’Kiya Jackson, who are students of St Mary’s Academy, recently gave a presentation of their findings at the American Mathematical Society south-eastern chapter’s semi-annual meeting in Georgia.

They were reportedly the only two high schoolers to give presentations at the meeting attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech. And they spoke about how they had 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. Legions of schoolchildren have learned the notation summarizing the theorem in their geometry classes: a²+b²=c².

As mentioned in the abstract of Johnson and Jackson’s 18 March mathematical society presentation, trigonometry – the study of triangles – depends on the theorem. And since that particular field of study was discovered, mathematicians have maintained that any alleged proof of the Pythagorean theorem which uses trigonometry constitutes a logical fallacy known as circular reasoning, a term used when someone tries to validate an idea with the idea itself.

Johnson and Jackson’s abstract adds that the book with the largest known collection of proofs for the 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 abstract counters, “that isn’t quite true”. The pair asserts: “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 theorem using trigonometry and without resorting to circular reasoning.

Johnson told the New Orleans television news station WWL it was an “unparalleled feeling” to present her and Jackson’s work alongside university researchers.

 

Comments

[Laurie]

I’ll have to check this out and share it with my students.