# Two US teens claim they have a new proof for Pythagoras' theorem

In other words, they say they could demonstrate the theorem without employing to circular reasoning and by simply utilising trigonometry.

Two New Orleans high school students Calcea Johnson and Ne’Kiya Jackson claim to have used trigonometry to demonstrate Pythagoras' theorem, something which scholars have believed to be impossible for 2000 years.

Pythagoras' theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. The theorem states that in a right triangle, the square of the length of the hypotenuse, the side opposite the right angle, is equal to the sum of the squares of the lengths of the other two sides, the legs.

This theorem has numerous applications and is used in designing bridges, buildings, and other structures.

As per the abstract by these two students, mathematicians have long insisted that any assertion that the Pythagorean theorem can be proved using trigonometry is logical fallacy. Logical fallacy, also known as circular reasoning, is the term used when someone tries to prove an idea with the idea itself. When this occurs, the end of an argument comes back to the beginning without proving itself.

US teens prove 2000-years-old Pythagoras's theorem through trigonometry

The book, The Pythagorean Proposition by Elisha Loomis, which contains the largest known collection of theorem proofs, “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem, " the abstract says.

In the abstract, they counter the arguments saying “that isn’t quite true.” The duo said, “We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry – the Law of Sines – and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1.”

In other words, they say they could demonstrate the theorem without employing to circular reasoning and by simply utilising trigonometry.

These girls, Jackson and Johnson of St Mary’s Academy, gave a presentation of their findings at the American Mathematical Society south-eastern chapter’s semi-annual meeting in Georgia.

During the meet, they both asserted that they have found out a new proof for the 2000-year old theorem.

Johnson told local media, “There’s nothing like it – being able to do something that people don’t think that young people can do. You don’t see kids like us doing this – it’s usually, like, you have to be an adult to do this.”

The two at the all-girls school in New Orleans's Plum Orchard area commended their teachers for pushing them to succeed in a task that mathematics had deemed impossible.

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