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Pythagorean Theorem and its Converse

Use a-squared plus b-squared equals c-squared to prove triangles are right triangles.

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The Man Behind the Theorem

Credit: Thomas Stanley
Source: http://commons.wikimedia.org/wiki/File:Pythagoras_in_Thomas_Stanley_History_of_Philosophy.jpg
License: CC BY-NC 3.0

He studied the skies, philosophical theories, and musical notes. He believed that numbers had unique personalities. He avoided beans because they looked too much like human fetuses. And he proved one of the most important geometric theories of all time. He was Pythagoras, of ancient Greece.

A Universe of Numbers

Today, we tend to remember Pythagoras as the brilliant mathematician who proved the Pythagorean theorem. However, during his lifetime, he was more widely known as the founder of a secret religious society that sought to understand the mysteries of the Universe. Born around 570 BCE, he grew up well educated. As a young man, he studied with Anaximander and Thales of Miletus, Greek scholars known for their contributions to mathematics, astronomy, and philosophy. On the recommendation of Thales, Pythagoras traveled to Egypt, where he spent ten years studying with priests and learning about local religious practices.

Upon his return to the Greek world, he founded a religious society dedicated to his philosophy, now referred to as Pythagoreanism. His disciples, known as the mathematikoi, lived and worked together. They followed strict rules of behavior, such as wearing white and not eating meat or beans. They had no personal possessions and kept their rituals and teachings secret from outsiders. Pythagoras and his followers believed that everything in the Universe revolved around numbers. Striving to make sense of the world through mathematics, they discovered geometric proofs. They found connections between numbers and music. They studied the stars to track the patterns of their movements. They believed that by studying math and adhering to the Pythagorean way of life, they could purify their souls and free themselves from a cycle of reincarnation.

Credit: Fyodor Bronnikov
Source: http://commons.wikimedia.org/wiki/File:Bronnikov_gimnpifagoreizev.jpg
License: CC BY-NC 3.0

No one is quite sure how Pythagoras died. According to one story, an angry mob attacked his secret society. He tried to flee, but a bean field blocked his way. Rather than risk reincarnation by touching the beans, he allowed his attackers to kill him. Other accounts claim that he managed to escape the attack on his community but died of starvation in exile. Pythagoras may have turned math into a religion, but he and his students made great strides in using it to understand the world.

See for yourself: http://www.youtube.com/watch?v=iBqEpC-dHqk

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Watch the videos below to learn more about the ancient history of the Pythagorean theorem, see an origami proof, and find out how the theorem is used in football.




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