Brief introduction to the history of European geometry

The history of European geometry is briefly described as follows:

Euclidean geometry refers to the geometric system defined by the ancient Greek mathematician Euclid. It is the most important geometry in the history of western mathematics and the cornerstone of traditional geometry. The basic concepts of Euclidean geometry are point, line, surface and angle, and the development direction of geometry is standardized on the basis of five postulates.

The development of Euclidean geometry can be traced back to the 3rd century BC. Euclid founded this geometric system by axiomatic method, and systematically expounded its basic ideas and theories in his book Geometry Elements.

In Euclidean geometry, all points on a straight line are considered to be equivalent, which establishes a clear relationship between points on the same straight line. At the same time, the angle concept in Euclidean geometry is also very important. For example, a right triangle with an included angle of 90 degrees can help us calculate the side length and angle.

In addition, Euclidean geometry has many important concepts and theorems, such as Pythagorean theorem, similar triangles, circle and so on. The development of Euclidean geometry provided an important foundation for later analytic geometry, non-Euclidean geometry and Riemannian geometry.

Postulate and axiom

1, any two points can be connected by a straight line.

2. Any line segment can be infinitely extended into a straight line.

3. Given any line segment, you can make a circle with an endpoint as the center and a line segment as the radius.

4. All right angles are equal.

5. If two straight lines intersect with the third straight line, and the sum of internal angles on the same side is less than the sum of two right angles, then the two straight lines must intersect on this side.