Solid geometry

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).

A solid figure is the region of 3D space bounded by a two-dimensional 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 (and other polyhedrons), cubes, cylinders, cones (and truncated cones).

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:

Advanced topics include:

• projective geometry of three dimensions (leading to a proof of Desargues' theorem by using an extra dimension)
• 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.

See also

• Euclidean geometry
• Shape
• Solid modeling
• Surface

Notes

References

• Kiselev, A. P. (2008). Geometry. Vol. Book II. Stereometry. Translated by Givental, Alexander. Sumizdat.

1. Constructive solid geometry
2. Octant (solid geometry)
3. Spherical geometry
4. Johnson solid
5. Outline of geometry
6. Solid angle
7. Euclidean geometry
8. Solid modeling
9. Cylinder
10. Boundary representation
11. Platonic solid
12. Solid Geometry (film)
13. Face (geometry)
14. Tinkercad
15. Pyramid (geometry)
16. Three-dimensional space
17. Rhombohedron
18. Quadrant (plane geometry)
19. Geometry
20. Heronian mean