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 of a sphere is proportional to the cube of its radius.
Basic topics in solid geometry and stereometry include
Advanced topics include
- projective geometry of three dimensions (leading to a proof of Desargues' theorem by using an extra dimension)
- further polyhedra
- descriptive geometry.
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 computer graphics.
- Kiselev, A. P. (2008). Geometry. Book II. Stereometry. Translated by Givental, Alexander. Sumizdat.