Note, since Pythagoras lived so long ago and there is little to no account of his early life. It was, however, believed that he was heavily influenced by Pherekydes, Thales, and Anaximander. Pythagoras became influential himself and was able to gather together a group of individuals who had the same beliefs as him. According to the encyclopedia he established “philosophical, political, and religious society whose members believed that the world could be explained using mathematics” (Atkins & Koth, 2002).
They had a huge belief of having only whole numbers and rational numbers. This group of individuals called themselves Pythagoreans and the school was called The School of Pythagoras. In the encyclopedia it goes on to say that their beliefs were secrecy, vegetarianism, refusal to eat beans, immortality, and even reincarnation. There are many other beliefs they had, but the main direction of Pythagoreans was “philosophy, mathematics, music, and gymnastics” it is also said that “reality is mathematical; philosophy is used for spiritual purification” and much more. The thing that sets this group apart from most, is that men and women were allowed to join, which was unheard of during this time period. One of the most famous theorem that came from Pythagoras and his followers was known as the Pythagorean Theorem. This theorem states that for any right triangle with legs of length a and b and hypotenuse if length c, then \(a^{2}+b^{2}=c^{2}\). A simple proof of this theorem could be constructed. Given a right triangle ABC, let angle \(ABC = 90^{\circ}\). Then, \(\sin(C) = \dfrac{AB}{AC}\) and \(\cos(C) = \dfrac{BC}{AC}\). Using the identity \(\sin^{2}(C)+\cos^{2}(C)=1\), then \((\dfrac{AB}{AC})^{2}+(\dfrac{BC}{AC})^{2}=1\). Therefore, after simplifying you will get \((AB)^{2}+(BC)^{2}=(AC)^{2}\) (Molokach). It is believed that one of Pythagoras’ followers, Hippasus of Metapontum, had discovered something that went against their beliefs. In the legend it is said that this person was also killed by the group because of what he discovered. In an article written by Brian Clegg, he shows the actual problem that Hippasus was working on (2009). According to stories Hippasus asked the question of how long is the diagonal of a 1x1 square. Using the Pythagoras Theorem, we can see that the answer to this problem is \(\sqrt{2}\). This is because \(1^{2}+1^{2}=c^{2}\), which implies \(c=\sqrt{1^{2}+1^{2}}=\sqrt{2}\). Since, this could not be simplified to a rational number it seemed to fail their beliefs. This in turn, probably, caused the Pythagoreans to kill Hippasus.
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## AuthorHello, as you may know my name is Kendrick Hardison. This blog will be used to share my experiences, teach things I may have learned, advise others, and much more. If you have any questions or if you would like for me to write a post on something you are interested in, click here to get to my contact page. WARNING: Math may show up smaller than normal text on mobile devices.## Archives
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