Geometry is concerned with the properties of space and of objects in space. Geometry is a mathematical system that is usually concerned with points, lines, surfaces, and solids. Different sets of assumptions give rise to different geometries.
Geometry deals with sets of points in a plane or in space.
In its most elementary form geometry is concerned with such metrical problems as determining the areas and diameters of two-dimensional figures and the surface areas and volumes of solids. The study of plane curves, angles, polygons, and lines is called plane geometry . The study of curves in three-dimensional space such as spheres, cones, cylinders, and polyhedra is called solid geometry . Other fields of geometry include analytic geometry, descriptive geometry, analysis situs or topology, the geometry of spaces having four or more dimensions, fractal geometry, and non-Euclidean geometry. Modern abstract geometry deals with very general questions of space, shape, size, and other properties of figures.