Solid geometry

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space.
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior.
Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms, cubes, cylinders, cones and other solids of revolution.

History

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.

Topics

Basic topics in solid geometry and stereometry include:

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.

Advanced topics include:

projective geometry of three dimensions
further polyhedra
descriptive geometry.
List of solid figures

Whereas a sphere is the surface of a ball, for other solid figures it is sometimes ambiguous whether the term refers to the surface of the figure or the volume enclosed therein, notably for a cylinder.

Techniques

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.

Applications

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

Solid geometry

History

Topics

List of solid figures

Techniques

Applications