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. 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