1, Pythagoras School Pythagoras School is a school founded by the ancient Greek mathematician Pythagoras, which mainly studies integers and irrational numbers. The Pythagorean school discovered irrational numbers, which they thought existed outside integers and could not be expressed by integer proportions.

2. eudoxus School, eudoxus School is a school founded by eudoxus, an ancient Greek mathematician, whose main research object is geometry. Eudoxus School found some geometric theorems, such as the parallel axiom, which proved that when two lines intersect with the same line, they either intersect at a point or do not intersect.

3. Hellenistic period. Hellenistic period was a school of mathematics founded by ancient Greek mathematicians Euclid and Archimedes, which mainly studied geometry and algebra. During this period, mathematicians discovered many new irrational numbers, such as π, E, etc. The discovery of these irrational numbers not only broadened mathematicians' horizons, but also provided a new direction for the development of mathematics in later generations.

The concept of irrational number

1, the main feature of irrational number is that it cannot be expressed by a finite decimal or integer. For example, one of the most common irrational numbers is infinite acyclic decimal π, and its value cannot be expressed by a finite decimal decimal fraction. Other irrational numbers can also be obtained in a similar way, such as the base e of natural logarithm, the golden ratio φ and so on.

2. The number of irrational numbers is mathematically countable, that is, irrational numbers can correspond to each other in a specific way. For example, we can sort all irrational numbers by length (that is, the number of digits after the decimal point), so as to get a complete one-to-one correspondence.

3. Besides the basic mathematical properties, irrational numbers also play an important role in many practical applications. In physics, the calculation results of many physical quantities are often irrational numbers that cannot be directly measured. These irrational numbers often appear in physics because some physical phenomena have infinite or infinitesimal characteristics and cannot be expressed by a finite decimal or integer.