---
tag: M225KZAV4F
kind: problem
name: Moser's circle problem
aliases: [circle-division-by-chords, circle-points-segments-proof, dividing-a-circle-into-areas]
sources:
  - wikipedia: en:399730@r1374440837
    locator: Moser's circle problem
    note: adopted
    mention: wikipedia://en/399730
    sections: [Problem]
same_as:
  wikidata: Q5284051
  wikipedia: Moser's circle problem
inventory: [H9WTV5BC9H]
---

## Problem

**Moser's circle problem** asks how many regions a circle can be divided into by choosing $n$ points along the circumference of the circle and joining each pair of points by a straight line. The greatest possible number of regions with $n$ points is given by

$$r_G = { n \choose 4 } + { n \choose 2 } + 1 = \frac{1}{24}(n^4 - 6 n^3 + 23 n^2 - 18 n + 24),$$