The theorem states that a right-angled triangle has an area on the side opposite the right angle the hypotenuse is equal to the complete sum of the squares of the other two sides. On his arrival in Croton, he quickly attained extensive influence, and many people began to follow him. Scholars still are not sure whether Pythagoras left the city before the violence broke out, whether he survived it, or whether he was himself killed during the uprising. Both his astronomical and geometrical theories seem to have naturally developed from the theories of the elder philosopher. According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. As a child Pythagoras spent his early years in Samos but travelled widely with his father. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem, as well as discoveries in the field of music, astronomy, and medicine.
There is disagreement among the biographers as to whether the Greek philosopher Pythagoras forbade all animal food, or only certain types. According to various accounts, the couple had a son named Telauges, and three daughters named Damo, Arignote, and Myia. His father, Mnesarchus, was a gem merchant. The lack of information by contemporary writers, together with the secrecy which surrounded the , meant that invention took the place of facts. There were no 'open problems' for them to solve, and they were not in any sense interested in trying to formulate or solve mathematical problems.
Pythagoras also invented the five regular solids. Certainly he was well educated, learning to play the lyre, learning poetry and to recite. Furthermore the initial answer did not answer the question. Additionally, Pythagoras and his followers developed their own theories about the cosmos. They were taught by Pythagoras himself and obeyed strict rules.
This had a great effect on future esoteric traditions, such as Rosicrucianism and Freemasonry , both of which were occult groups dedicated to the study of mathematics and both of which claimed to have evolved out of the Pythagorean brotherhood. It was his belief that the number system, and therefore the universe system, was based on the sum of these numbers: ten. The Pythagoreans observed a rule of silence called echemythia, the breaking of which was punishable by death. He also believed that the human soul is immortal and after death it moves into another living being, sometimes an animal. He died in Metapontum around 90 years old from unknown causes.
Pythagoras set up an organization which was in some ways a school, in some ways a brotherhood and here it should be noted that sources indicate that as well as men there were many women among the adherents of Pythagoras , and in some ways a monastery. A major Pythagoras accomplishment was the discovery that music was based on proportional intervals of four. Very strict rules of conduct governed this cultural center. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. Pythagoras also related music to mathematics. Anaximander certainly was interested in geometry and and many of his ideas would influence Pythagoras's own views. Much of their mysticism concerning the soul seem inseparable from the Orphic tradition.
He also studied properties of numbers which would be familiar to mathematicians today like even and odd numbers. While the theorem that now bears his name was known and previously utilized by the Babylonians and Indians , he, or his students, are often said to have constructed the first proof. The Pythagorean Theorem has many proofs. Everything of the kind mentioned by Plato and Aristotle is attributed not to Pythagoras, but to the Pythagoreans. One of Pythagoras's major accomplishments was the discovery that music was based on proportional intervals of the numbers one through four.
When the Pythagorean school in Croton closed, she emigrated to Athens. At the age of eighteen, Pythagoras traveled to Miletus to meet Thales, a master of mathematics and astronomy. At first, the school was highly concerned with the morality of society. Pythagoras discovered that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth. He became known as the Father of Geometry many years after publishing a thirteen volume work called Euclid's Elements in which he compiled and explained all the known mathematics of his time. Pythagoras' famous theorem states that the sum of the square of the shorter sides of a right triangle is equal to the square of the longer side, which is the hypotenuse.
This is unlikely, since the commonly accepted dates for the two lives do not overlap. Pythagoras asserted he could write on the moon. The prohibition on beans could be linked to favism , which is relatively widespread around the Mediterranean. This went against Pythagoras's philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became immortal. His beliefs eventually led to the Copernican theory of the universe. Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of followers around himself called Pythagoreans.