Discrete geometry

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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
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

Discrete geometry

Topics in discrete geometry

See also