Born: Approximately 569 BC
Birth place: Samos Greece
Founder of a philosophical and religious school
Died: Approximately 500 – 475 BC
Died At Age – About 70 – 95
Location of death: Metapontum Italy
Pythagoras is repeatedly referred to as the first pure mathematician. He was born on the island of Samos, Greece in 569 BC. Various writings place his death between 500 BC and 475 BC in Metapontum, Lucania, Italy. His father, Mnesarchus, was a gem merchant. His mother’s name was Pythais. Pythagoras had two or three brothers.
A little historians say that Pythagoras was married to a woman named Theano and had a daughter Damo, and a son named Telauges, who succeeded Pythagoras as a teacher and possibly taught Empedocles. Others say that Theano was one of his students, not his wife, and say that Pythagoras never married and had no children.
Pythagoras was well educated, and he played the lyre throughout his lifetime, knew poetry and recited Homer. He was interested in mathematics, philosophy, astronomy and music, and was greatly influenced by Pherekydes (philosophy), Thales (mathematics and astronomy) and Anaximander (philosophy, geometry).
In 520 BC, Pythagoras, now a free man, left Babylon and back to Samos, and sometime later began a school called The Semicircle. His methods of teaching were not popular with the leaders of Samos, and their desire for him to become involved in politics did not appeal to him, so he left.
Pythagoras established in Crotona, a Greek colony in southern Italy, about 518 BC, and founded a philosophical and religious school where his many supporters lived and worked. The Pythagoreans lived by rules of activities, including when they spoke, what they wore and what they ate. Pythagoras was the Master of the society, and the followers, both men and women, who also lived there, were known as mathematikoi. Pythagoras believed:
All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics.
The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Pythagoras believed that both mathematics and music could purify.
Numbers have personalities, characteristics, strengths and weaknesses.
The world depends upon the interaction of opposites, such as male and female, lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow.
Certain symbols have a mystical significance.
All members of the society should observe strict loyalty and secrecy.
Pythagoras eventually wrote down the theories, teachings and discoveries of the group, but the Pythagoreans always gave credit to Pythagoras as the Master for:
1. The sum of the angles of a triangle is equal to two right angles.
2.The theorem of Pythagoras for a right angled triangle : The square on the hypotenuse is equal to the sum of the squares on the other two sides.
The Babylonians understood this 1000 years earlier, but Pythagoras proved it.
Constructing figures of a given area and geometrical algebra. For example they solved various equations by geometrical means.
The innovation of irrational numbers is certified to the Pythagoreans, but seems not likely to have been the idea of Pythagoras as it does not support with his philosophy the all things are numbers, since number to him destined the ratio of two whole numbers.
The five normal solids (tetrahedron, cube, octahedron, icosahedron, dodecahedron). It is thought that Pythagoras knew how to make the first three but not last two.
Pythagoras trained that Earth was a sphere in the center of the Kosmos (Universe), that the planets, stars, and the universe were spherical as the sphere was the majority perfect solid figure. He also skilled that the paths of the planets were circular. Pythagoras accepted that the morning star was the same as the evening star, Venus.
Pythagoras studied odd and even numbers, triangular numbers, and perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra.
Pythagoras is also attributed with the finding that the intervals between harmonious musical notes for all time have whole number ratios. For example, playing half a length of a guitar string gives the similar note as the open string, but an octave higher; a third of a length gives a different but harmonious note; etc. Non-whole number ratios, on the other hand, tend to give discordant sounds. In this way, Pythagoras described the first four overtones which build the common intervals which have become the primary building blocks of musical harmony: the octave (1:1), the perfect fifth (3:2), the perfect fourth (4:3) and the major third (5:4). The oldest way of tuning the 12-note chromatic scale is known as Pythagorean tuning, and it is based on a stack of perfect fifths, each tuned in the ratio 3:2.
The mystical Pythagoras was so thrilled by this discovery that he became influenced that the whole universe was based on numbers, and that the planets and stars moved according to mathematical equations, which corresponded to musical notes, and thus produced a kind of symphony, the “Musical Universalis” or “Music of the Spheres”.