Like something out of a movie (hidden figures) For over 2,000 years, such proofs were considered impossible. And yet, undeterred, I mentioned in the previous page the time for change. We shouldn't be waitnging on Shakespeares to tell us how to write (that being said you shouldn't be writing any less than shakspear) or Einstein to tell us how to think, again don't think any less than Einstein, anyway you get my point. This is the true essence of going to school. its never been a routine it has always been the passion to think to learn.Who said you have to be an academia for years and years before you can actually produce some new mathematics. I am truly humbled when I read stories of todays students making history. How amazing and how it brings me to tears Ne’Kiya Jackson and Calcea Johnson published hMathematical proofs of sequences of statements that demonstrate an assertion is true or false.

 

 

Pythagoras’ theorem

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— a2 + b2 = c2, relating the length of a right triangle’s hypotenuse to those of its other two sides — has been proven many times with algebra and geometry h in 1927, mathematician Elisha Loomis asserted that the feat could not be done using rules from trigonometry, a subset of geometry that deals with the relationships between angles and side lengths of triangles. He believed that Pythagoras’ theorem is so fundamental to trigonometry, any trigonometry-based attempt to prove the theorem would have to first assume it was true, thereby resorting to circular logic. Jackson and Johnson conceived the first of their trigonometry-based proofs in 2022, while seniors at St. Mary’s Academy in New Orleans, a Catholic school attended mostly by young Black women. At that time, only two other trigonometric proofs of Pythagoras’ theorem existed, presented by mathematicians Jason Zimba and Nuno Luzia in 2009 and 2015, respectively. Working on the early proofs “sparked the creative process,” Jackson says, “and from there we developed additional proofs.” .After formally presenting their work at an American Mathematical Society meeting in March 2023, the duo set out to publish their findings in a peer-reviewed journal. “This proved to be the most daunting task of all,” they said in the paper. In addition to writing, the duo had to develop new skills, all while entering college. “Learning how to code in LaTeX [a typesetting software] is not so simple when you’re also trying to write a 5-page essay with a group, and submit a data analysis for a lab,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


MOTIVATED TO FINISH WHAT THEY STARTED
 

It was important to me to have our proofs published to solidify that our work is correct and respectable,” Johnson says. According to Jackson and Johnson, trigonometric terms can be defined in two different ways, and this can complicate efforts to prove Pythagoras’ theorem. By focusing on just one of these methods, they developed four proofs for right triangles with sides of different lengths and one for right triangles with two equal sides.Among these, one proof stands out to Lozano-Robledo. In it, the students fill one larger triangle with an infinite sequence of smaller triangles and use calculus to find the lengths of the larger triangle’s sides. “It looks like nothing I’ve ever seen,” Lozano-Robledo says.Jackson and Johnson also leave another five proofs “for the interested reader to discover,” they wrote. The paper includes a lemma — a sort of stepping-stone to proving a theorem — that “provides a clear direction towards the additional proofs,” Johnson says.

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