Discrete Geometry
Polytopes, packings, coverings, and incidence geometry.
Discrete Geometry. Polytopes, packings, coverings, and incidence geometry.
Foundations and canonical references
The standard treatments of discrete geometry approach the subject from complementary angles. Matousek, Lectures on Discrete Geometry (2002) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for discrete geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2002Lectures on Discrete Geometrymatousek-2002
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Explore
- 01
Polytope Theory
Face structure, f-vectors, and the upper bound theorem.
- 02
Sphere Packings and Lattices
Densest packings, kissing numbers, and Viazovska's E8 / Leech results.
- 03
Incidence Geometry
Szemerédi–Trotter and the polynomial method.
- 04
Convex Geometry
Brunn–Minkowski theory, isoperimetric inequalities, and asymptotic convex geometry.
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