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Calcea Johnson and Ne’Kiya Jackson Pythagorean Theorem Proof Is A Black American Breakthrough
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Calcea Johnson and Ne’Kiya Jackson Pythagorean Theorem Proof Is A Black American Breakthrough
On March 24th, 2023, St. Mary’s Academy New Orleans Students Calcea Johnson and Ne’Kiya Jackson announced they came up with a breakthrough in math history: they solved the Pythagorean Theorem, but in a novel way. Now, for anyone to have achieves another new way of solving the Pythagorean Theorem is news worthy, but for two African American teenagers to do it is should be a headline story in a World media obessed with the crazy idea that if you’re young and black, you’re always doing something wrong.
Calcea Johnson and Ne’Kiya Jackson are to be celebrated, but first, we have to get the confusiton over what they did out of the way. Contrary to the story that:
Calcea Johnson and Ne’Kiya Jackson, high schoolers at St. Mary’s Academy, have proven Pythagoras’ Theorem without circular logic, according to WWL-TV. The mathematical discovery is said to have not been proven by mathematicians for 2,000 years.
The truth is that the Pythagorean theorem has been solved many ways. Johnson and Jackson discovered another way that was not thought possible. But, what’s the Pythagorean theorem, to start with? Well, when I learned it in school, it was the idea that in a given right triangle, the square one can form from the right line is equal in size to adding the squares formed by bottom line of that right triangle, and the slanted line on the left side of the same right triangle. Or it looks like this:
Now, if you were paying attention in school, you recognized that diagram, even if you didn’t really understand why it was important. Well, that mathematical theorem has been proven many ways using different methods. But all of those approaches involved using some form of the diagram above. The idea that the Pythagorean theorem without a diagram was considered not possible. Have a look at this seven-year-old example seen in Stack Exchange of thought before Johnson and Jackson came along:
A: There are some proofs of Pythagoras theorem which don’t even require high school maths to understand, but they all are using shapes to prove of the theorem. However, I am trying to find some proofs of Pythagoras theorem that don’t use shapes in their proofs, for example a purely algebraic proof. Besides, they would still be easy enough to teach for students with high school level of knowledge in mathematics.
My question: Prove that for ?2+?2=?2
there are infinity many triples in ℤ+ fit into the equation? – which requires high school maths knowledge to understand.
Reponses:
1. You’re trying to prove a geometrical theorem without using geometry?
2. How do you define a right-angled triangle in an analytic/algebraic way?
And the examples claiming to do so were observered as actually having nothing to do with the Pythagorean theorem.
Finally, another observer wrote “You could try to use something like this, (using Arc length
which is the distance between two points along a section of a curve) but as you’ll see, it would be a circular argument, because in the derivation of these results the Pythagorean theorem is already used. You could just Define arc-length to be the linked expression, but then I think you’ll loose your high school students.” But it’s at the place regarding the use of “ a circular argument” where Johnson and Jackson’s finding takes flight, because they proved a circular argument could work. That stands in stark contrast to the age old idea that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem.”
Here’s the research duo’s abstract (https://ift.tt/ujJivGa
In the 2000 years since trigonometry was discovered it’s always been assumed that any alleged proof of Pythagoras’s 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.” But that isn’t quite true: in our lecture 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 \sin^2x + \cos^2x = 1.
Now, I have not seen Calcea Johnson and Ne’Kiya Jackson’s research paper to give you a full presentation of what they showed to the American Mathematical Society. But what they presented was impressive enough for the American Mathematical Society to encourage them to present their findings in a peer-reviewed journal.
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