Circle

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	$\pi{}r^2$
Height	diameter: $2r$
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.

The points on a circle are all points $(x,y)$ such that

• $x^2+y^2=r^2$

where r is the radius of the circle.

Special Properties

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.

External links

• Wikipedia Contributors. "Circle".
• Hi.gher.Space Wiki Contributors. "Circle".