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.
Analytic geometry is the study of geometry using algebraic methods.
Analytic geometry combines the generality of algebra with the precision of geometry. It is sometimes called Cartesian geometry , after Descartes , who was the first to exploit the methods of algebra in geometry. Analytic geometry addresses geometric problems from an algebraic point of view by associating any curve with variables by means of a coordinate system. Differential geometry applies techniques of calculus and studies such local properties as tangents and curvature . Topology , developed in the 20th century, is a study of generalized geometric elements and such properties as connectedness and compactness .