- Solid geometry
mathematics, solid geometry was the traditional name for the geometryof three-dimensional Euclidean space— for practical purposes the kind of spacewe 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.
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.
Archimedes, Demiurge, Johannes Kepler, planimetry, Plato, Timaeus (dialogue)
"...paraphrased and taken in part from the
1911 Encyclopædia Britannica"
Basic topics of solid geometry
Basic topics are:
* incidence of planes and lines
dihedral angleand solid angle
* the cube,
tetrahedronand other pyramids
octahedron, dodecahedron, icosahedron
* cones and cylinders
quadrics: spheroid, ellipsoid, paraboloidand hyperboloids.
More advanced are the study of
projective geometryof three dimensions leading to
* proof of
Desargues' theoremby using an extra dimension
descriptive geometry. Analytic geometryand 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.
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Look at other dictionaries:
solid geometry — n. the branch of geometry dealing with solid, or three dimensional, figures … English World dictionary
solid geometry — noun the geometry of 3 dimensional space • Topics: ↑mathematics, ↑math, ↑maths • Hypernyms: ↑geometry * * * noun : a branch of geometry that deals with the figures of three dimensional space * * * the geometry of solid figures; geometry of three… … Useful english dictionary
solid geometry — geometry which deals with three dimensional objects … English contemporary dictionary
solid geometry — the geometry of solid figures; geometry of three dimensions. [1725 35] * * * … Universalium
solid geometry — sol′id geom′etry n. math. the geometry of solid figures; geometry of three dimensions • Etymology: 1725–35 … From formal English to slang
solid geometry — /sɒləd dʒiˈɒmətri/ (say soluhd jee omuhtree) noun the geometry of solid figures; geometry of three dimensions … Australian English dictionary
solid geometry — noun Date: 1733 a branch of geometry that deals with figures of three dimensional space … New Collegiate Dictionary
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