SEMESTER PROJECT

The full definition of the Pythagorean Theorem, including the hypothesis, is as follows: Given a right triangle with legs a and b and hypotenuse c, a²+b²=c². This theorem is used to find an unknown length. While that length is usually the hypotenuse, this theorem can also be used to find either of the legs. The converse of the Pythagorean theorem is also true, and it is used to test if a triangle is a right triangle. The converse is stated as the following: ''if a triangle has sides of length a, b, and c, and if a²+b²=c², then the angle opposite the side of length c is a right angle.'' Euclid proved the Pythagorean theorem as well as its converse in his book Elements, which will be shown later.

The creation of the Pythagorean theorem is first credited to Pythagoras (569-475 BC), a Greek mathematician who is said to be one of the first mathematicians in history. He studied with western philosophers Thales and Anaximander, and his work later influenced other philosophers, such as Plato and Aristotle. Pythagoras believed numbers were the way to truth and truth itself (Bernholc, 2011; Mark, 2019).

Pythagoras organized a religious/scientific school, or monastery, where the members held strict rules including wear white clothes, observe sexual purity, do not touch beans, practice vegetarianism, and much more. The members also held a strict vow of secrecy. Because of this secrecy, the first proof of the Pythagorean theorem is unknown, as well as if Pythagoras wrote it. The theorem could have likely been written by his followers years after he died, but the theorem is still accredited to him (Britannica, 2022).

Scientists have discovered tablets dating to over 1000 years before Pythagoras was born that show the Babylonians were using Pythagorean triples for surveying land. Pythagorean triples are positive integers that satisfy the Pythagorean theorem, such as (3-4-5), (5-12-13), or even (9-40-41). The possible integers that create Pythagorean triples are endless. While the tablets do not explicitly state the Pythagorean theorem, they do show that the Babylonians understood the concept of the theorem through the use of triangles with legs of a length equivalent to 1 in our number system and a hypotenuse with a length of \(\sqrt 2\) (CK-12 Foundation).

Egyptians may have used the concept of the Pythagorean theorem while constructing their pyramids. The Egyptians used a rope with twelve evenly spaced knots that could be formed into a (3-4-5) triangle, with one angle being 90°. It is believed that other various ancient civilizations had their own understanding and uses of the Pythagorean theorem as well, many years before Pythagoras was born (CK-12 Foundation).