Pythagoras was born on the Aegean island of Samos (an island in eastern Greece today). He was smart and studious since childhood, and studied geometry, natural science and philosophy with famous teachers. After longing for the wisdom of the East, he came to Babylon, India and Egypt through Qianshan Mountain, absorbed the rich nutrition of Arab civilization, Indian civilization and even China civilization, and returned to Samos Island around 530 BC. Later, he moved to Croton, southern Italy, and founded his own school, engaged in education and mathematics research.
Pythagoras and his school have many creations in mathematics, especially interested in the changing law of integers. For example, a number whose sum of all factors (except itself) is equal to itself is called a perfect number (such as 6,28,496, etc.). ), and the number greater than its factor is called abundance; The number less than the sum of its factors is called deficit. They also found that "the sum of the squares of two right angles of a right triangle is equal to the square of the hypotenuse", which is called Pythagorean Theorem in the West and Pythagorean Theorem in China. Now there is the concept of Pythagorean ternary array, which refers to the collection of three arrays, which can be used as three sides of a right triangle.
In geometry, the Pythagorean school proved that the sum of the interior angles of a triangle is equal to two right angles. Studied the golden section; The method of regular pentagon and similar polygon was found. It is also proved that there are only five regular polyhedrons-regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron and regular icosahedron.
Pythagoras school thinks that numbers are the noblest and most mysterious, and they mean integers. "Number is everything", that is to say, all kinds of relationships in the universe can be expressed by integers or the ratio of integers. However, a student named hippasus found that the diagonal of a square with a side length of 1 cannot be expressed by the ratio of integers. This violates the creed of this school, so it stipulates a law: no one is allowed to reveal the secret of existence (that is, irrational numbers). Naive hippasus inadvertently told others about his discovery and was killed. But it soon caused a great revolution in mathematical thought. In the history of science, this incident is called "the first mathematical crisis". Hippasus's lesson to the martyrs is that science has no end. Whoever delimits the forbidden zone for science will become the enemy of science and eventually be buried by science.