Discrete geometry.html



Discrete geometry or combinatorial geometry may be loosely defined as study of geometrical objects and properties that are discrete or combinatorial, either by their nature or by their representation; the study that does not essentially rely on the notion of continuity.

Parts of its domain of research is often attributed to other kinds of geometry: digital geometry, computational geometry,finite geometry. It also overlaps with convex geometry and combinatorial topology.

(The term combinatorial geometry has also been used as a synonym for simple matroid, but that is no longer popular.)

Topics in discrete geometry

• Polytopes and polyhedral combinatorics
• Packing, covering and tiling
  • Kepler's conjecture (Johannes Kepler, 1611): The densest way to pack identical spheres in a given space is the "cannonball" arrangement, i.e., in flat layers, with each sphere resting upon three touching spheres beneath it.
• Triangulation
• Pick's theorem
• Sperner's lemma
• Topological combinatorics
• Discrete differential geometry
• Geometric set partitioning
• Geometric set transversals

See also

• Discrete mathematics
• Paul Erdős

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