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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
A collection of unit circles and the corresponding unit disk graph. In geometric graph theory, a unit disk graph is the intersection graph of a family of unit disks in the Euclidean plane. That is, it is a graph with one vertex for each disk in the family, and with an edge between two vertices whenever the corresponding vertices lie within a ...
The unit circle is the Cayley absolute that determines a metric on the disk through use of cross-ratio in the style of the Cayley–Klein metric. In the language of differential geometry, the circular arcs perpendicular to the unit circle are geodesics that show the shortest distance between points in the model.
Penny graphs have also been called unit coin graphs, [2] because they are the coin graphs formed from unit circles. [1] If each vertex is represented by a point at the center of its circle, then two vertices will be adjacent if and only if their distance is the minimum distance among all pairs of vertices.
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n , between points. [ 1 ]
The disk covering problem asks for the smallest real number such that disks of radius () can be arranged in such a way as to cover the unit disk. Dually, for a given radius ε , one wishes to find the smallest integer n such that n disks of radius ε can cover the unit disk.
In probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform for all angles. Description [ edit ]
For example, the quadratic form , when set equal to one, produces the unit hyperbola, which plays the role of the "unit circle" in the plane of split-complex numbers. Similarly, the quadratic form x 2 {\displaystyle x^{2}} yields a pair of lines for the unit sphere in the dual number plane.