Solid geometry

In mathematics, solid geometry or stereometry is the traditional name for the geometry of three-dimensional, Euclidean spaces[1] (i.e., 3D geometry).

Stereometry deals with the measurements of volumes of various solid figures (or 3D figures), including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.[2]

The Pythagoreans dealt with the regular solids, but the pyramid, prism, cone and cylinder were not studied until the Platonists. Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height. He was probably also the discoverer of a proof that the volume enclosed by a sphere is proportional to the cube of its radius.[3]

Whereas a sphere is the surface of a ball, it is sometimes ambiguous whether the term refers to the surface of the figure or the volume enclosed therein, notably for a cylinder. The following table includes major types of shapes that either constitute or define a volume.

Various techniques and tools are used in solid geometry. Among them, analytic geometry and vector techniques have a major impact by allowing the systematic use of linear equations and matrix algebra, which are important for higher dimensions.

A major application of solid geometry and stereometry is in 3D computer graphics.