Last year GNN reported on two Louisiana high schoolers who used trigonometry to properly demonstrate Pythagoras’ Theorum, a mathematical concept that remained unsolved for more than 2,000 years.
Ne’Kiya Jackson and Calcea Johnson made national headlines, won their school a large grant, and were invited to publish papers on their discovery after making it.
On October 28th, in a paper published by the teens in the journal American Mathematical Monthly, they’ve used their skills in trigonometry to demonstrate 9 other ways to prove the theory.
To understand the scope of their accomplishment, it’s necessary first to understand the theory.
Pythagoras’ Theorem deals with triangles that are not perfectly symmetrical, and it goes like this.
The area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. It is written as a2+b2=c2.
One of the interesting things about this equation is that for 2,000 years, no mathematician has been able to demonstrate the truth of it without simply using the equation itself as proof; what is called circular logic, and not accepted as true evidence of proof.
It was this sticky problem that the teens solved, and in doing so won their academy a large grant from NBA legend and all-around great guy, Charles Barkley.
“To have a paper published at such a young age — it’s really mind-blowing,” Johnson, who is now studying environmental engineering at Louisiana State University, said in a statement emailed to Live Science. “I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things.”
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According to Johnson and Jackson, they proved the theory correct without using it as proof like this. Trigonometry is the study of triangles, and presenting equations through it can be done through the principles of sine and cosine. Sine and cosine are ratios that are defined in the context of a triangle’s right angle.
However, according to the young women, over time these two principles have merged in an unhelpful way.
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“Students may not realize that two competing versions of trigonometry have been stamped onto the same terminology,” the pair write in their introduction. “In that case, trying to make sense of trigonometry can be like trying to make sense of a picture where two different images have been printed on top of each other.”
Beyond this explanation, readers can take a look at the presentation in the study and see for themselves whether they can make sense of the concepts. In any case, by teasing sine and cosine apart, one can find “a large collection of new proofs of the Pythagorean theorem.”
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