A pair of senior high schoolers were able to prove the Pythagorean theorem using trigonometry at an American Mathematical Society (AMS) meeting. The feat they pulled off was something that mathematicians never knew was possible.
Trigonometry To Prove Pythagorean Theorem?
Live Science notes that, though their proof needs to be further reviewed by mathematicians, it would be quite impressive if confirmed.
This discovery was made by Calcea Johnson and Ne'Kiya Jackson, who are both seniors at St. Mary's Academy in New Orleans. They showed their findings during the AMS Spring Southeastern Sectional Meeting.
The Pythagorean theorem serves as a trigonometric basis and a mathematical cornerstone. It holds that adding the squares of the two shorter sides of a right triangle will equal the square of the right triangle's hypotenuse. Popular Mechanics reports that, for several centuries, this notion has been proven by some of the greatest minds in history, including Albert Einstein and US President James Garfield.
There have been hundreds of proofs regarding this popular theorem. However, very few- if any- were independently grounded in trigonometry. This is because the theorem's fundamentals are what trigonometry grounds itself on. Hence, using trigonometry to prove it may be considered circular reasoning, as it is essentially using the theorem itself to prove its existence.
Interestingly, the teen duo was reportedly able to prove the theorem without employing the actual theorem. However, since their findings are yet to undergo peer review, mathematicians have yet to see if their findings will stand.
The duo presented a proof of the theorem that is based on the Law of Sines. They demonstrate that this evidence is independent from "the Pythagorean trigonometric identity sin2x+cos2x=1." Simply stated, the pair claimed that they were able to prove the theorem with trigonometry and without falling into the pit of circular reasoning.
Calcea Johnson and Ne’Kiya Jackson, students of St Mary’s Academy, say they have proven Pythagoras’s theorem by using... Posted by American Mathematical Society on Monday, March 27, 2023
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Young Mathematicians
As per Business Insider, Catherine Roberts, who is the AMS' executive director, encouraged these young mathematicians to submit their discoveries to a journal for further review. Ms. Roberts notes that the AMS celebrates how these young mathematicians shared their work.
In an interview with the WWL news station of New Orleans, Johnson expressed how unparalleled the feeling is and how they were able to do something that people do not usually think young people can execute. Johnson adds that people do not usually see young individuals like them doing something that they did. The duo was quite excited to simply be part of the process.
While these findings are quite impressive, it is not the first time for mathematicians to use sine and cosine to prove the theorem without depending on "sin2x+cos2x=1." Nevertheless, this does not make Johnson and Jackson's findings fall short.
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