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. But a student named hippasus found that the diagonal (root 2) 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 discipline: no one can reveal the secret of the existence of the root number 2 (that is, irrational number). Naive hippasus inadvertently told others about his discovery and was killed. But the root number 2 soon caused a great revolution in mathematical thought. In the history of science, this incident is called "the first mathematical crisis". The lesson that Hippaso's martyrdom left for Root 2 is that science has no end. Whoever delimits the forbidden zone for science will become the enemy of science and be buried by science at last.
Unfortunately, Pythagoras, who was full of vigor and vitality, not only tended to be conservative academically, but also opposed new things politically, and finally died.
Among the early mathematicians in ancient Greece, Pythagoras had the greatest influence. His legendary life left many magical legends to future generations.
Pythagoras was born in Samos (now an island in eastern Greece) and died in Tarrington (now taranto in southern Italy). He is a philosopher, mathematician and astronomer. When he was young, he went to study in Babylon and Egypt according to the practice of rich children at that time, which was directly influenced by eastern civilization. After Pythagoras returned to China, he founded a secret academic group integrating politics, religion and mathematics, which was called Pythagoras School by later generations. The activities of this school are secret and shrouded in an incredible mysterious atmosphere. It is said that every freshman must swear to secrecy and only join this school for life. Another habit of the school is to attribute all inventions to the leaders of the school and keep them secret so that future generations don't know who invented them and when.
Pythagorean Theorem (Pythagorean Theorem) is another contribution of Pythagoras. One of his students, hippasus, discovered irrational numbers through Pythagorean theorem. Although this discovery broke Pythagoras' belief that everything in the universe is the ratio of integers, and led to hippasus's tragic death, the theorem played a great role in promoting the development of mathematics. In addition, Pythagoras also made some contributions to music, astronomy and philosophy, and initiated the theory of the earth circle, which holds that the sun, the moon and the five stars are all spheres floating in space.
Short stories:
Pythagoras was once invited to a dinner of a rich politician. The host's luxurious palace-like restaurant is covered with square and beautiful marble floor tiles. These hungry VIPs complained bitterly because the big meal was delayed. This mathematician, who is good at observing and understanding, stares at these square tiles with regular arrangement and beautiful scale, but Pythagoras not only appreciates the beauty of tiles, but also thinks about their relationship with [numbers], so he picks up a brush, squats on the floor, selects a tile and draws a square with its diagonal AB as the edge. He found that the area of a square is exactly equal to the sum of the areas of two tiles. He was curious, so he made another square with the diagonal of the rectangle made of two tiles. He found that the area of this square is equal to the area of five tiles, which is the sum of the square areas with two sides. So far, Pythagoras has made a bold assumption: the square of the hypotenuse of any right triangle is exactly equal to the sum of the squares of the other two sides. That meal, the ancient Greek mathematician, never left the ground.