---
tag: P9CM4GQ2T0
kind: concept
name: Sphere
msc: [51M05, 51M04]
sources:
  - url: https://en.wikipedia.org/wiki/Sphere
same_as:
  wikidata: Q12507
  wikipedia: Sphere
---

## Summary

A sphere is the set of points at a fixed positive distance, the radius, from a fixed point, the centre.
In three-dimensional [[Euclidean space|0XPR1E85W0]] it is the surface of a ball, and in the plane it is a [[circle|060W5CBZP6]].
The same definition makes sense in any [[metric space|0VKD1TP7F3]].
Spheres are among the most symmetric shapes, and many problems of geometry, physics and analysis are posed on them.

## Explanations

### L1 human

Think of the skin of a ball: every point on it is the same distance from the middle.
That common distance is the radius, and the middle point is the centre.
For example, the points $(x, y, z)$ with $x^2 + y^2 + z^2 = 1$ form the sphere of radius $1$ about the origin.
In the plane the same recipe draws a circle.