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Pythagoras
Pythagoras was a Greek philosopher that was responsible for some devolpments in mathematics. He was born around 560 B.C. and died around 480 B.C. He was originally from the city of Samos, Ionia(Later day Italy), but moved away from his home to escape the tyranny of Polycrates. Ionia was an area around the Mediterranean Sea and Samos was an island inside that area. From Samos he moved to the city of Croton. In Croton he established a school. The school was a philosophical and religious school. This school practiced secrecy so not very many records survived and little is known. Students of Pythagoras' school were called Pythagoreans. These Pythagoreans believed that everything could be reduced to numbers. They said that all things are numbers.
The Pythagoreans studied triangles with the ratio 3:4:5. They noticed that all 3:4:5 triangles are right triangles. Using that triangle, Pythagoreans came up with the Pythagorean Theorem. He stated that the square of the hypotenuse equals the squares of the other two sides. In the 3:4:5 triangle, 5 is the hypotenuse. 3 and 4 are the legs. The angle opposite of the hypotenuse is a right angle. Since the hypotenuse squared equals the two legs squared, the equation should be:
Example without the 3:4:5 triangle:
Although the theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier he may have been the first to prove it (Maxwell, Seth) Of Pythagoras actual work nothing is known. It is hard to tell the difference between his work and the work of his students.
Pythagoras and his followers also noticed that the vibrating strings of an instrument made balanced tones when the strings were whole numbers. These ratios of the lengths could be extended to other instruments as well.
Pythagoras's school had many followers. When students were new to his school they were not allowed to talk for three years. This included class disscussions. After the first three years of schooling the students were allowed to speak and join in on discussions. Usaully only males went to his school, but occasionally a female attended. When a female did go to his school they were not allowed to join in the discussions even after three years of schooling.
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