# Geometry and Pythagorean Theorem

• Updated March 27, 2023
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As high school and middle school students progress through their Geometry or Trigonometry class, they often see the familiar equation, a2+b2=c2, in their textbooks. Through the Greek philosopher, mathematician, and religious advocate, Pythagoras, students globally incorporate this theorem into their math curriculum. Although Pythagoras’ most well-known revelation was the creation of the Pythagorean Theorem, his Greek philosophical ideas, additional mathematical discoveries, and his involvement in religious rules and culture cannot be overlooked.

Pythagoras was born in Samos, Ionia during 570 BCE, which is a small Greek island in the Mediterranean Sea. It was thought that his name was connected to Pythia, a sacred sanctuary for one of the Olympian gods Apollo, who apparently prophesied to Pythagoras’ mother that her child will hold many important characteristics which would help human society in the future. Pythagoras was taught by three philosophers, who would eventually teach him about mathematical and various philosophical ideas.

Compared to many other Greek mathematicians, who have detailed records of their lives, Pythagoras followed a religious code of secrecy which made it difficult to find information on his early life. However, sources have found out that he was musically and academically educated and was fond of learning poetry. Later in his teen and adult life, he would pull inspiration from philosopher Thales and philosopher Anaximander’s mathematical ideas regarding geometry and astronomy. Advice from these philosophers would also lead to his departure from Samos to Egypt, where he would further expand his knowledge of mathematical ideas.

Through scholarship records, Pythagoras learned how to speak Egyptian directly through the Pharaoh of Egypt. During his stay in Egypt, he learned the basics and functions of geometry which would later prove to be worthy in his future findings regarding math. Pythagoras also had a religious brotherhood of followers, who would have to follow strict laws, such as his idea of secrecy, refusal to eat beans and boycotting of animal-skinned clothing.

There was a diverse debate over who taught Pythagoras arithmetic ideas. Some thought that through the lectures from Egyptian priests or visits to the temple, Pythagoras was able to learn geometry. However, others think that a group of Mediterranean citizens, such as the Phoenicians, were responsible for Pythagoras’ knowledge of arithmetics.

Later in 532 BCE, Pythagoras would move to the city of Italy, Crotons, where he would found a philosophical and religious school where his followers would have to adhere to the strict rules, such as that reality is mathematical in nature, philosophy can be used for spiritual purification, the soul can rise to union with the divine, certain symbols have a mystical significance, and that all brothers and sisters of the order should observe strict loyalty and secrecy.

Pythagoras’ interest in geometrical shapes led him to make his most well-renowned contributions to math – the Pythagorean Theorem, Pythagorean Triples, and the sums of the internal and external angles of polygons. The Pythagorean Theorem states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the square of the two other legs. Pythagoras also discovered, what everyone calls today, Pythagorean Triples, which are three positive integers that fit perfectly into the Pythagorean Theorem. Finally, he also uncovered that the sum of the interior angles of any polygon is equal to 2n-4 right angles, n being the number of sides; similarly, he recognized that the sum of the exterior angles of any polygon is equal to four right angles, regardless of how many sides it has.

We have used the developments Pythagoras made in trigonometry in chapter 7 in our textbook. The Pythagorean Theorem shows up in the very beginning of chapter 7 where it introduces the formula and makes us apply it to sin, cosine, and tangent. We started with the simple formula, a2+b2=c2, and began to apply it to even more complicated concepts like finding values of trigonometric functions from a right triangle. Because of Pythagoras’ significant developments and discoveries, we are able to solve different varieties of problems and take what we learned into higher levels of math.

Cite this paper

Geometry and Pythagorean Theorem. (2021, Jul 23). Retrieved from https://samploon.com/geometry-and-pythagorean-theorem/

FAQ

## FAQ

Is the Pythagorean Theorem used in geometry?
The Pythagorean Theorem is used in geometry to find the length of the hypotenuse of a right triangle.
What did Pythagoras discover in geometry?
Pythagoras discovered that the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides.
Why Pythagorean Theorem is important in geometry?
The Pythagorean Theorem is important in geometry because it is a way to find the length of a side of a right triangle.
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