1. Properties of points, lines, surfaces and bodies: This is the basis of geometry, including the definitions of points, lines, surfaces and bodies and their basic properties, such as length, area and volume.
2. Classification and construction of geometric figures: This includes the study of various geometric figures (such as triangles, quadrilaterals, polygons, circles, etc.). ) and how to construct geometric figures satisfying specific properties according to given conditions.
3. Geometric transformation: This includes geometric transformations such as translation, rotation and reflection, as well as the properties and applications of these transformations.
4. Space geometry: This includes the positional relationship between straight lines and planes in space, as well as the positional relationship between points, lines, surfaces and bodies in space.
5. Analytic geometry: This is a subject that transforms geometric problems into algebraic problems. This paper mainly studies the representation of points, lines, surfaces and bodies in the coordinate system and their relationships.
6. Non-Euclidean geometry: This is a geometric system different from Euclidean geometry, which mainly studies the space with negative curvature.
7. Differential geometry: this is a kind of geometry that studies the properties of curves and surfaces, mainly studying the tangents, normals and curvatures of curves and surfaces.
8. Topological geometry: This is a kind of geometry that studies the continuity of space, mainly focusing on the connectivity and compactness of space.
The above is the main research content of mathematical geometry. Different research fields will have different research methods and tools, but they are all inseparable from the study of spatial form and position.