Solid geometry
From Wikipedia, the free encyclopedia
- This article is about the geometric shape. For the short film starring Ewan McGregor, see Solid Geometry (film).
In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. It was developed following the development of plane geometry. Stereometry deals with the measurements of volumes of various solid figures: cylinder, circular cone, truncated cone, sphere, prisms, blades, wine casks.
The Pythagoreans had dealt with the sphere and 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, and was probably the discoverer of a proof that the volume of a sphere is proportional to the cube of its radius.
See also: Archimedes, Demiurge, Johannes Kepler, planimetry, Plato, Timaeus (dialogue)
...paraphrased and taken in part from the 1911 Encyclopædia Britannica
[edit] Basic topics of solid geometry
Basic topics are:
- incidence of planes and lines
- dihedral angle and solid angle
- the cube, cuboid, parallelepiped
- the tetrahedron and other pyramids
- prisms
- octahedron, dodecahedron, icosahedron
- cones and cylinders
- the sphere
- other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids.
[edit] Other topics
More advanced are the study of
- projective geometry of three dimensions leading to
- proof of Desargues' theorem by using an extra dimension
- further polyhedra
- descriptive geometry.
Analytic geometry and vector techniques have a major impact by allowing the systematic use of linear equations and matrix algebra; this becomes more important for higher dimensions. A major reason to study this subject is the application to computer graphics, meaning that algorithms become important.
