Search results
Results From The WOW.Com Content Network
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.
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. Table of solutions, 1 ≤ n ≤ 20 [ edit ]
The problem addressed by the circle method is to force the issue of taking r = 1, by a good understanding of the nature of the singularities f exhibits on the unit circle. The fundamental insight is the role played by the Farey sequence of rational numbers, or equivalently by the roots of unity :
In the complex plane, the most obvious circle inversion map (i.e., using the unit circle centered at the origin) is the complex conjugate of the complex inverse map taking z to 1/z. The complex analytic inverse map is conformal and its conjugate, circle inversion, is anticonformal.
This algebraic function can be written as the right side of the solution equation y = f(x). Written like this, f is a multi-valued implicit function. Algebraic functions play an important role in mathematical analysis and algebraic geometry. A simple example of an algebraic function is given by the left side of the unit circle equation:
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 ...
for example: z = 4 + 5i, where x and y are real numbers, and i is the imaginary unit. In this customary notation the complex number z corresponds to the point ( x , y ) in the Cartesian plane ; the point ( x , y ) can also be represented in polar coordinates with:
Cayley transform of upper complex half-plane to unit disk. On the upper half of the complex plane, the Cayley transform is: [1] [2] = +.Since {,,} is mapped to {,,}, and Möbius transformations permute the generalised circles in the complex plane, maps the real line to the unit circle.