Two young, mathematically proficient female scientists have achieved a goal long considered nearly impossible in the professional world.Image: Shutterstock

Two young scientists, well versed in mathematics, achieved what had long been considered virtually impossible in the professional world: they proved the famous Pythagorean theorem (a2 + b2 = c2) using trigonometry – and proved it many times a little.

Their results were published in the journal American Mathematical Monthly. The crux of the matter is this: Trigonometry is a branch of geometry whose basic formulas are based on the assumption that the Pythagoras theorem is true. There is therefore a risk of circular argumentation – that is, a proof that what is to be proved is already a prerequisite.

The publisher says that without circular reasoning, professional mathematicians have only managed to come up with such a proof twice. Additionally, there are hundreds of other proofs of the Millennium Theorem from other mathematical disciplines such as algebra.

### What is the Pythagorean Theorem about?

The Pythagorean Theorem is probably one of the few formulas that many people still remember by heart from their school curriculum. This is about the relationship between the side lengths of a right triangle: the sum of the squares of the right sides (a and b) is equal to the square of the hypotenuse (c), which is the side opposite the 90-degree angle. Therefore, if you know the lengths of the other two sides of a right triangle, you can calculate the length of any side of the right triangle.

### new evidence

In their now published work, authors Calcea Johnson and Ne'Kiya Jackson propose five ways to prove this theorem using trigonometry. There is also a way to provide five additional proofs. Roughly speaking, to do this, they formed various new right triangles with specific angular masses from right triangle ABC.

In 2022, the two came up with the idea during a math competition in an American high school. One problem is to create a new proof for the Pythagorean theorem. “The $500 prize motivated us to take on this task,” they wrote. “The task turned out to be much more difficult than we initially thought, and we spent many long nights trying but failing to provide proof.”

### Praise for Michelle Obama

For months, the teenage girls sacrificed their free time to complete the project, even participating during the holidays. “There were many times when we wanted to give up on the project, but we decided to persevere and finish what we started.” In the end, in addition to the award, there was even a gift from former first lady Michelle Obama, according to the publisher. praise. Now there's a scientific publication containing new evidence.

“I'm so proud that we can all have such a positive impact,” said co-author Johnson. The authors show that young women are capable of doing this and “in doing so let other young women know that they can do anything they want to do.”

Johnson is now studying environmental engineering at Louisiana State University and Jackson is studying pharmacy at Xavier University of Louisiana. (Sudanese Development Authority/Department of Political Affairs)

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