Combinatorial geometry - Definition

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. It also overlaps with convex geometry and combinatorial topology.

Topics in discrete geometry

• Combinatorial convexity
• 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
• Geometric set partitioning
• Geometric set transversals

Related articles

• Discrete mathematics
• Paul Erdös.