# Circle

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Circle | |
---|---|

Dimensions | 1 |

Connected | Yes |

Compact | Yes |

Euler characteristic | 0 |

Orientable | Yes |

Symmetry | SO(1) |

Disk | |
---|---|

Rank | 2 |

Space | Spherical |

Notation | |

Tapertopic notation | 2 |

Toratopic notation | (II) |

Bracket notation | (II) |

Elements | |

Edges | 1 circle |

Measures (radius r) | |

Area | |

Height | diameter: |

Central density | 1 |

Related polytopes | |

Dual | Disk |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 1 |

Orientable | Yes |

Properties | |

Symmetry | O(2) |

Convex | Yes |

Nature | Tame |

A **circle**, also known as a **1-sphere** is the set of all points on a 2D plane that are a certain distance away from a given point. This distance is called the radius. Circles are not considered to be polygons, as they cannot be meaningfully assigned any elements other than points.

A circle is the 1-dimensional hypersphere.

Formally, a filled-in circle is called a *disk*, and its boundary is called a *circle*. A disk is the 2-dimensional hyperball.

## Coordinates[edit | edit source]

The points on a circle are all points such that

where *r* is the radius of the circle.

## Special Properties[edit | edit source]

Circles have many unique properties among the 2D shapes. These include:

- They are rotationally symmetric from every angle.
- They have the lowest perimeter-to-area ratio of any closed 2D shape.
- Their center of mass's cycloid is a straight line.