Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
Discrete geometry has large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology.
Read more about Discrete Geometry: History, Topics in Discrete Geometry
Famous quotes containing the words discrete and/or geometry:
“The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.”
—W.V. Quine (b. 1908)
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)