
Have you ever seen this equation a^{2} + b^{2} = c^{2}? It from the Pythagorean Theorem. If given a right triangle, a triangle with one angle equaling 90 degrees, you can use this formula to figure out the measurements of the sides of the triangle. The sum of the squares of the two shorter sides equals the hypotenuse squared. If the two shorter sides of the triangle were 3 units (a) and 4 units (b), you can calculate the hypotenuse which would be third side (c). The sum of 3 units squared (nine) and 4 units squared (sixteen) equals twentyfive. The square root of twentyfive is five, therefore the third side of the triangle is 5 units long. This theorem is a notable contribution to mathematics for which Pythagoras is known. Pythagoras was born between the years of 585 to 569 B.C.E. in Samos, an Aegean island. He left Samos at the age of eighteen to study in Phoenicia, Egypt, and possibly Babylonia. He died around 500 B.C.E. During his lifetime, Pythagoras founded a school in Croton. The school stressed four disciplines: arithmetica (number theory), hormonia (music), geometra (geometry), and astrologia (astronomy). The Pythagorean society members were sworn to secrecy. Members were not allowed to discuss information of the disciplines with others outside the society. Information was transferred through word of mouth instead of written accounts to ensure this secrecy. By law, women were not allowed to attend public meetings but they were admitted to the Master's lectures. It was said that there were at least twentyeight females in a special category of mathematici (mathematicians). Among these women was Theano who Pythagoras later married. Not only was the school founded on mathematical principles but on religious principles as well. The members of the Pythagorean community were vegetarians. It was their belief that the soul of a person could inhabit the body of another person or animal. They would not wear garments made of wool for it was also an animal product. Pythagoras's death is unknown. Some say he died in a revolt in which the meeting place of the Pythagoreans was surrounded and set to fire, of which only a few survived. Others say the members formed a bridge using their bodies over the flames to allow Pythagoras to escape. He fled to Metapontum where he chose to die at the hands of his enemies rather than trample over a sacred bean field. Since there are no written documents regarding Pythagoras and his teachings, it is hard to say what is true and what is myth. However, beside the Pythagorean Theorem, Pythagoras is given credit as playing an important part of the development of music by discovering the harmonious intervals of the musical scale. His discovery of the octave, he found the fifth, the fourth, and the whole tones proved that mathematics play a large role in musical thought. Using two string with the same degree of tension, by dividing a string exactly in half (a ratio 2:1) the shorter string gives off a tone that is an octave higher than the longer string. Using the ratio 2:3 the pitch is called a fifth. The pitch using a ratio 3:4 is called a fourth. The ratio 9:8 is a pitch called a whole tone. Pythagoreans were able to determine mathematically the intonation, or pitch, for an entire musical system.

Contributed by CiCi Naifeh

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