Group

Convex and Discrete Geometry

This group gathers theorems about convex bodies, lattices, and finite configurations of points and shapes, the branch of geometry concerned with packing, covering, counting, and combinatorial arrangement rather than continuous curvature. It covers sphere-packing results, including the Kepler conjecture, classical convexity theorems such as Helly's, Radon's, and Caratheodory's theorems on convex hulls, lattice-point results including Pick's theorem, and further combinatorial-geometric results, including the Sylvester-Gallai and Erdos-Anning theorems, that constrain how points and lines can be arranged.

Facts

Comparison

Era Of Emergence

1890 1

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All Convex and Discrete Geometry

Convex and Discrete Geometry

16 entries

Convex and Discrete Geometry

16 entries

Branch

Topic Area

Proved

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Statement Form

Sources

1. Discrete Geometry (Wikipedia)

WikipediaHistory section

Quote, History section

Polyhedra and tessellations had been studied for many years by people such as Kepler and Cauchy, modern discrete geometry has its origins in the late 19th century.

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Convex and Discrete Geometry

All Convex and Discrete Geometry

Art Gallery Problem

Barbier's Theorem

Beck's Theorem (Geometry)

Blaschke-Santalo Inequality

Caratheodory's Theorem (Convex Geometry)

Caratheodory's Theorem (Convex Hull)

Crystallographic Restriction Theorem

Double Bubble Theorem

Erdos-Anning Theorem

Helly's Theorem

Isoperimetric Inequality

Kawasaki's Theorem

Kepler Conjecture

Pick's Theorem

Radon's Theorem

Sylvester-Gallai Theorem