Science Fair Project Encyclopedia
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.
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.
...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, parallelepiped
- the tetrahedron and other pyramids
- octahedron, dodecahedron, icosahedron
- cones and cylinders
- the sphere
- other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids.
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.
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