Discrete geometry

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.