The development history of Greek mathematics can be divided into three periods. The first period lasted from Ionian school to Plato school, from the middle of the 7th century BC to the 3rd century BC. The second period is the pre-Alexandria period, from Euclid to 65438 BC+046 BC when Greece fell into Rome. The third period was the later period of Alexandria, which was ruled by Romans and ended when 64 1 Alexandria was occupied by Arabs.

Map of ancient Greece

Let's talk about the first phase of the school:

Pythagoras school

Pythagoras was born in Samos (an island in eastern Greece today) around 580 BC. In order to get rid of tyranny, he moved to Croton in the southern part of the Italian peninsula. Organize a secret society that integrates politics, religion, philosophy and mathematics. Later, it was destroyed in the political struggle and Pythagoras was killed, but his school continued to exist for two centuries (about 500 ~ 300 BC). This school tries to explain everything with numbers, not only thinking that everything contains numbers, but also thinking that everything is numbers.

Pythagoras

They are famous for discovering Pythagorean Theorem (called Pythagorean Theorem in the West), thus discovering incommensurable metrics. Another feature of this school is the close connection between arithmetic and geometry. They found a formula that three positive integers represent the lengths of three sides of a right triangle, and noticed that the continuous odd numbers starting from 1 must be square numbers and so on. This is not only an arithmetic problem, but also related to geometry. They also found five regular polyhedrons. Astronomy pioneered the earth circle theory, which holds that the sun, the moon and the five stars are all spheres, floating in space. Pythagoras is also the originator of music theory.

Ionian school

This school is significantly different from Pythagoras school. The former studies mathematics not only for philosophical interests, but also for practical purposes. The latter does not pay attention to practical application, and connects mathematics with religion, hoping to explore eternal truth through mathematics.

Homo sapiens school

In the 5th century BC, Athens became the center of cultural gathering, and people advocated the spirit of openness. In an open discussion or debate, you must have knowledge of eloquence, rhetoric, philosophy and mathematics, so the "Homo sapiens School" (or the translation school's clever debate and philosopher school) came into being. They teach grammar, logic, mathematics, astronomy, rhetoric, eloquence and other subjects. In mathematics, they put forward "three big problems":

① Divide any angle equally;

(2) Cubes, that is, making a cube, so that its volume is twice that of known cubes;

(3) Turn a circle into a square, that is, find a square so that its area is equal to the known circle.

The difficulty of the problem is that only rulers (rulers without scales) and compasses are allowed to be used in drawing. The interest of the Greeks lies not in actual drawing, but in solving these problems theoretically under the constraints of rulers and rulers. This is an important step in the transition of geometry from practical application to system theory. An Tifeng of this school (about 430 BC) put forward the "exhaustive method" to solve the problem of turning a circle into a square, which is the embryonic form of modern limit theory. First, a circle is inscribed with a square, then the number of sides is doubled, and a polygon of 8,16,32 is obtained. In this way, An Tifeng is convinced that the "difference" between the "last" polygon and the circle will be exhausted. This provides an approximate method for finding the area of a circle, which coincides with China's separatist thought (about 263 years ago).

Plato school

Plato (about 427 BC ~ 347 BC) founded the school in Athens and established the Academy. He attaches great importance to mathematics, but unilaterally emphasizes the role of mathematics in training intelligence and ignores its practical value. He advocates cultivating logical thinking ability through the study of geometry, because geometry can give people a strong intuitive impression and embody abstract logical laws in concrete graphics. This school has trained many mathematicians. For example, eudoxus studied under Plato, and he founded the theory of proportion, which was the predecessor of Euclid. Plato's student Aristotle was also a great philosopher in ancient times and the founder of formal logic. His logical thought paved the way for arranging geometry in a strict logical system in the future.

Plato

(The content is transferred from the mathematical latitude and longitude network, with deletion ~)