Discrete geometry | Wikipedia audio article

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00:00:49 1 History
00:01:26 2 Topics in discrete geometry
00:01:36 2.1 Polyhedra and polytopes
00:02:26 2.2 Packings, coverings and tilings
00:03:43 2.3 Structural rigidity and flexibility
00:04:10 2.4 Incidence structures
00:05:40 2.5 Oriented matroids
00:06:14 2.6 Geometric graph theory
00:06:48 2.7 Simplicial complexes
00:07:23 2.8 Topological combinatorics
00:08:15 2.9 Lattices and discrete groups
00:09:37 2.10 Digital geometry
00:10:13 2.11 Discrete differential geometry
00:11:03 3 See also



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SUMMARY
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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 a 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.