High school students may have just discovered an ‘impossible’ proof to the 2,000-year-old Pythagorean theorem

The two high school students high five each other. — Calcea Johnson and Ne’Kiya Jackson introduced their findings March 18 on the American Mathematical Society’s (AMS) Spring Southeastern Sectional Assembly. (Picture credit score: YouTube screenshot from WWL-TV)

Two highschool college students say they’ve proved the Pythagorean theorem utilizing trigonometry — a feat mathematicians thought was unimaginable.

Whereas the proof nonetheless must be scrutinized by mathematicians, it could represent a formidable discovering if true.

Calcea Johnson and Ne’Kiya Jackson, who’re seniors at St. Mary’s Academy in New Orleans, introduced their findings March 18 on the American Mathematical Society’s (AMS) Spring Southeastern Sectional Assembly.

“It is an unparalleled feeling, actually, as a result of there’s nothing prefer it — with the ability to do one thing that individuals do not assume that younger folks can do,” Johnson informed the New Orleans tv information station WWL (opens in new tab). “You do not see children like us doing this — it is normally, like, you need to be an grownup to do that.”

Pythagoras‘ 2,000-year-old theorem, which states that the sum of the squares of a proper triangle’s two shorter sides is the same as the sq. of the hypotenuse, is the idea for trigonometry. Trigonometry, which comes from the Greek phrases for triangle (“trigonon”) and to measure (“metron”), lays out how the aspect lengths and angles in a triangle are associated, so mathematicians thought that utilizing trigonometry to show the concept would all the time embody some hidden expression of the concept itself. Thus, proving the concept with trigonometry would represent a failure of logic referred to as round reasoning.

Remarkably, Johnson and Jackson say they’ll show the concept with out utilizing the concept itself. As a result of the findings haven’t but been accepted right into a peer-reviewed journal, nevertheless, it is nonetheless too quickly to say whether or not their proof will finally maintain up.

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Of their summary (opens in new tab), Johnson and Jackson quote from a 1927 e book by the American mathematician Elisha Loomis (1852 to 1940) referred to as “The Pythagorean Proposition (opens in new tab),” which incorporates the most important identified assortment of proofs of the concept — 371 options, in line with analysis revealed within the Journal of Concentrating on, Measurement and Evaluation for Advertising and marketing (opens in new tab). “There are not any trigonometric proofs, as a result of all the basic formulae of trigonometry are themselves based mostly upon the reality of the Pythagorean Theorem,” Loomis wrote.

However “that is not fairly true,” the youngsters wrote within the summary. “We current a brand new proof of Pythagoras’s Theorem which is predicated on a basic lead to trigonometry — the Regulation of Sines — and we present that the proof is unbiased of the Pythagorean trig id sin2x+cos2x=1.” In different phrases, the highschool seniors stated they’ll show the concept through the use of trigonometry and with out round reasoning.

“It’s uncommon for highschool college students to current at an AMS Sectional Assembly,” Scott Turner, director of communications at AMS (opens in new tab), informed Reside Science in a ready assertion.

Regardless of their younger age, the AMS has inspired the excessive schoolers to submit their findings to a scientific journal. “Following their convention presentation, their subsequent step could be to look into submitting their work to a peer-reviewed journal, the place members of our neighborhood can study their outcomes to find out whether or not their proof is an accurate contribution to the arithmetic literature,” Catherine Roberts (opens in new tab), government director at AMS, stated within the assertion.

Johnson and Jackson’s achievement has not gone unnoticed in math circles. “We have a good time these early profession mathematicians for sharing their work with the broader arithmetic neighborhood and we encourage them to proceed their research in arithmetic,” Roberts added.

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