Pythagoras of Samos lived in Ancient Greece from 560-480 B.C. He was born on the island of Samos according to Herodotus. It is now a part of the country Turkey. His father's name was Mnesarchus and mother's name was Pythais. Little is known about his childhood, but he probably had at least two brothers. He studied with the Babylonian group of astronomers called the Chaldaeans and was taught by the learned men of Syria in Tyre. The Chaldaeans discovered that the moon travels at different speeds in its orbit around the earth, but they could not explain why. His teacher at home was the philosopher Pherekydes.
He was influenced by Thales (the first of the wise men of ancient Greece) in his teen years. He was probably influenced by Anaximander, who had an interest in geometry and cosmology. Anaximander thought that the earth was the center of the universe and a cylinder. Pythagoras continued his education in Egypt in about 535 B.C. He became extremely proficient in mathematics and science while studying with the Babylonians in Babylon. He returned to Samos, which was now under the rule of Darius of Persia. He took a trip to Crete to study their legal system.
He returned to Samos and founded a school called Semicircle. The people of Samos did not think much of his teaching methods. Iamblichus wrote in Life of Pythagoras: "He tried to use his symbolic method of teaching which was similar in all respects to the lessons he had learnt in Egypt. The Samians were not very keen on this method and treated him in a rude and improper manner." In Southern Italy, Pythagoras founded a school called Kroton. It was a scientific as well as a religious community. The doctrine of the Pythagoreans was that all things are numbers. The early Pythagoreans explained the properties of numbers using certain arrangements of dots.
He made important discoveries in mathematics, astronomy, and music. His school of Pythagoreans is credited with the first proof of the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle will equal the sum of the squares of the other two sides. A right triangle is a triangle in plane geometry with one angle equal to 90 degrees. Algebraically, it is stated a^2+b^2=c^2, where a, b are the two sides and c is the side called the hypotenuse (the side opposite the angle with 90 degrees). They also discovered irrational numbers, which are real numbers that cannot be expressed as the ratio of two integers. Pythagoras led the way to the discoveries of Plato, Aristotle, and Copernicus. Plato especially thought very highly of Pythagoras’ ideas.
In astronomy, Pythagoras found that the sphere was the perfect shape. He also discovered that the Earth was a sphere. He erroneously taught that the earth was the center of the universe. He found that the moon’s orbit was inclined to the equator of the Earth. He also discovered that the planet Venus was both the evening star and morning star.