
In
mathematics, solid geometry is the traditional name for the
geometry of
three-dimensional Euclidean space (i.e., 3D geometry).
Stereometry deals with the
measurements of
volumes of various solid figures (three-dimensional figures), including
pyramids,
prisms and other
polyhedrons;
cylinders;
cones;
truncated cones; and
balls bounded by
spheres.
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.
[Paraphrased and taken in part from the ''1911 Encyclopædia Britannica''.]
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 (leading to a proof of
Desargues' theorem by using an extra dimension)
* further
polyhedra
*
descriptive geometry.
Solid figures
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.
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.
See also
*
Ball regions
*
Euclidean geometry
*
Dimension
*
Point
*
Planimetry
*
Shape
*
Lists of shapes
*
Surface
*
Surface area
*
Archimedes
Notes
References
*
{{DEFAULTSORT:Solid Geometry
*
Solid geometry