Solid geometry

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 studied as a sequel to plane geometry. Stereometry deals with the measurements of volumes of various solid figures: cylinder, circular cone, truncated cone, sphere, prisms, blades, wine casks.

History

The Pythagoreans had dealt with the sphere and regular solids, but the pyramid, prism, cone and cylinder were but little known until the Platonists took them in hand. Eudoxus established their mensuration, proving the pyramid and cone to have one-third the content of a prism and cylinder on the same base and of the same height, and was probably the discoverer of a proof that the volumes of spheres are as the cubes of their radii.

See also: Archimedes, Demiurge, Johannes Kepler, planimetry, Plato, Plato's Timaeus

...partly from the 1911 Encyclopaedia Britannica

Basic topics of solid geometry

Basic topics are:

• incidence of planes and lines
• dihedral angle and solid angle
• the cube, cuboid, parallelopiped
• the tetrahedron and other pyramids
• prisms
• octahedron, dodecahedron, icosahedron
• cones and cylinders
• the sphere
• other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids.

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.