PYTHAGORAS AND THE PYTHAGOREAN THEOREM
In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse).Pythagoras is one of the most influentual Greek philosophers, and one of history's most influential mathematicians, he helped lay the ground work that Archimedes and other mathematicians would build on -- including Sir Isaac Newton, one of the Renassiance discoverers of Calculus. Pythagoras is also responsible for founding musicology and music theory.
Pythagoras was born in Samos, and later he would go on to found the Pythagorean school of Philosophy. The Pythagorean school was a religious and philosophic school which had a lasting influence on religion and philosophy -- including Gnostic and Aesthetic Christianity. Pythagoras was instructed in the Ionian school of thought and eventually made his way to Egypt where he was instructed by the Egyptian priesthood. Because of his disgust over the Tyranny of Polycrates, Pythagoras was exiled from Samos. Having moved to Italy, he founded the Pythagorean school in which men and women would flock to. However, Pythagoras' life on Earth came to an end when the Democratic party won out in Italy and the Aristocratic Pythagoreans attacked the Democrats and Pythagoras died in the struggle.
Accomplishments by Pythagoras:
- The Pythagorean Theorem is attributed to him. Necessarily, the history between Pythagoras and his theorem is quite complex.
- Pythagoras introduced the concept of reincarnation to the Greeks through the idea of mentempsychosis.
- A music theory that says that music is based on proportional intervals of four.
- The theory that the Universe is base 10. Including the postulation of a tenth planet, known as Gorea (see John Norman's novels).
- Pythagoras discovered the theory of mathematical proportion.
- Proposed that the Earth was a sphere that revolved on it's own axis.
- Killed a student for his discovery of irrational numbers.
- Plato: Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According to R. M. Hare, his influence consists of three points: a) the platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. b) there is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science and morals". c) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both have been influenced by Orphism.
- Roman Influence: n the legends of ancient Rome, Numa Pompilius, the second King of Rome, is said to have studied under Pythagoras. This is unlikely, since the commonly accepted dates for the two lives do not overlap.