Two young scientists with an affinity for mathematics achieved what was long considered virtually impossible in the professional world: they proved the famous Pythagorean theorem (a² + b² = c²) using trigonometry – and did it several times.
The bottom line: Trigonometry is a branch of geometry, and its basic formulas are based on the assumption that the Pythagorean theorem is true. There is a risk of a so-called circular argument – that is, a proof in which what needs to be proven is already a condition.
Without circular reasoning, professional mathematicians have only managed to produce such a proof twice, the publisher said. In addition, there are hundreds of other proofs of the millennia-old theorem from other disciplines of mathematics, such as algebra.
Most people know it from school
The Pythagorean theorem is probably one of the few formulas that many people still have in the back of their minds during school lessons. This is about the relationship between the side lengths of a right triangle: The sum of the squares of the sides of the right angle (a and b) is equal to the square of the hypotenuse (c), which is opposite 90. -degree angle. So you can calculate the length of each side of a right triangle if you know the lengths of the other two sides.
In their now published article, Calcea Johnson and Ne’Kiya Jackson presented five ways to prove the theorem using trigonometry. There is also a method that allows for five additional proofs. To do this, they roughly formed several new right triangles with certain angular dimensions from a right triangle ABC.
Mathematics competition as a starting point
The two came up with the idea as students in 2022 during a math competition at their high school in the US. One question was to create a new proof for the Pythagorean theorem. “$500 in prize money motivated us to take on this task,” they write.
“The task proved much more difficult than we had initially imagined, and we spent many long nights trying and failing to produce a proof,” said Johnson and Jackson, whose work was published in American Mathematical Monthly.
Lob of ex-First Lady Obama
For months, the teenage girls sacrificed their free time to the project, even working on it while on vacation. “There were many moments when we both wanted to give up on the project, but we decided to persevere and finish what we started.” Ultimately, according to the publisher, in addition to the prizes, there was even praise from former First Dame Michelle Obama.
“I’m very proud that we can both have such a positive impact,” says co-author Johnson. The two authors showed that young women are capable of this and “let other young women know that they can do anything they want to do,” Obama said.
Johnson is now studying environmental engineering at Louisiana State University and Jackson is studying pharmacy at Xavier University of Louisiana.
Source: Krone
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