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Two students who discovered a seemingly insufferable proof to the Pythagorean theorem in 2022 have wow the mathematics community again with nine completely raw solution to the problem .
While still in high schooltime , Ne’Kiya Jackson and Calcea Johnson from Louisianaused trigonometry to prove the 2,000 - twelvemonth - old Pythagorean theorem , which posit that the sum of the square of a ripe triangle ’s two short sides are adequate to the lame of the triangle ’s longest side ( the hypotenuse ) . Mathematicians had long thought that using trig to leaven the theorem was unworkable , given that the fundamental formulas for trigonometry are based on the assumption that the theorem is straight .
Ne’Kiya Jackson and Calcea Johnson came up with an “impossible” proof to the Pythagorean theorem when they were high school seniors.
Jackson and Johnson came up with their " impossible " trial impression in answer to a incentive question in a school math contest . They presented their work at an American Mathematical Society meeting in 2023 , but the cogent evidence had n’t been thoroughly scrutinise at that point . Now , a new paper print Monday ( Oct. 28 ) in the journalAmerican Mathematical Monthlyshows their result held up to equal review . Not only that , but the two students also outlined nine more proofs to the Pythagorean theorem using trig .
" To have a paper published at such a young age — it ’s really idea - blowing , " Johnson , who is now consider environmental engineering at Louisiana State University , said in a statement e-mail to Live Science . " I am very proud that we are both able-bodied to be such a positive influence in point that young women and fair sex of color can do these thing . "
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By provingPythagoras ' theorem using trig , but without using the theorem itself , the two untested fair sex overcome a bankruptcy of logic known as orbitual reasoning . trig is a branch ofmathematicsthat lays out how the side , length and slant in a triangle are related , and as such , the discipline often includes look of the Pythagorean theorem . But Jackson and Johnson managed to try the theorem using a result of trigonometry called the Law of Sines , dodge rotary logical thinking .
In the new field of study , and on top of their initial cogent evidence , the young mathematicians draw four raw ways to try out Pythagoras ' theorem using trigonometry , as well as a refreshing method acting that uncover five more proofs , number 10 proofs .
Jackson and Johnson are only the third and quaternary citizenry know to have establish the Pythagorean theorem using trigonometry and without resorting to circular abstract thought . The two other people were professional mathematician , according to the statement .
" I did n’t think it would go this far , " Jackson , who presently studies pharmacology at the Xavier University of Louisiana , say in the argument . " I was middling surprised to be bring out . "
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In the theme , Jackson and Johnson say there are two ways to present trig and its purpose sine and cosine , but these versions are often conflated into one . Sine and cos are ratios that are define in the context of a triangle ’s correct slant , and they can be presented according to either the trigonometric method or a method acting that use polynomials of complex numbers , accord to the paper .
The conflation signify that " essay to make sense of trig can be like attempt to make sense of a scene where two different images have been printed on top of each other , " Jackson and Johnson indite .
By rally the two method apart , research worker can discover " a large collection of new proofs of the Pythagorean theorem , " the young mathematicians added .
If you wish reading this chronicle , here are some math books you might also enjoy :
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