---
tag: Q0RW86P85F
kind: concept
name: Discrete geometry
msc: [52C99, 52C10, 52C35]
sources:
  - url: https://en.wikipedia.org/wiki/Discrete_geometry
same_as:
  wikidata: Q906377
  wikipedia: Discrete geometry
---

## Summary

Discrete geometry is the part of geometry that studies finite or discrete configurations of simple objects, such as points, lines, circles, polygons and convex bodies.
Its questions are combinatorial: how many incidences, distances or intersections such configurations can have.
Typical topics are [[tilings|GKJK293DXS]], [[sphere packings|HF32CBN5MA]], [[polytopes|QP7GEKDTYX]], incidence problems and geometric graphs.
It is closely tied to convex geometry and to computational geometry.

## Explanations

### L1 human

Discrete geometry asks counting questions about shapes placed in the plane or in space.
How many pairs among $n$ points can be at distance exactly $1$?
How many lines through at least two of the points must there be?
How densely can equal coins be packed on a table?
Such questions are easy to state, but many of them are still open.