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These graphs have a vertex for each circle or disk, and an edge connecting each pair of circles or disks that have a nonempty intersection. Unit disk graphs may be formed in a different way from a collection of equal-radius circles, by connecting two circles with an edge whenever one circle contains the center of the other circle.
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. In topology, it is often denoted as S 1 because it is a one-dimensional unit n-sphere ...
Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself. Without further specifications, the term unit disk is used for the open unit disk about the origin , D 1 ( 0 ) {\displaystyle D_{1}(0)} , with respect to the standard ...
This group has six mirror planes, each containing two edges of the cube or one edge of the tetrahedron, a single S 4 axis, and two C 3 axes. T d is isomorphic to S 4, the symmetric group on 4 letters, because there is a 1-to-1 correspondence between the elements of T d and the 24 permutations of the four 3-fold axes.
Once again we begin with two copies of the z-plane, but this time each one is cut along the real line segment extending from z = −1 to z = 1 – these are the two branch points of g(z). We flip one of these upside down, so the two imaginary axes point in opposite directions, and glue the corresponding edges of the two cut sheets together.
English: All of the six trigonometric functions of an arbitrary angle θ can be defined geometrically in terms of a unit circle centred at the origin of a Cartesian coordinate plane.
A plane segment or planar region (or simply "plane", in lay use) is a planar surface region; it is analogous to a line segment. A bivector is an oriented plane segment, analogous to directed line segments. [a] A face is a plane segment bounding a solid object. [1] A slab is a region bounded by two parallel planes.
A circle that passes through the center O of the reference circle inverts to a line not passing through O, but parallel to the tangent to the original circle at O, and vice versa; whereas a line passing through O is inverted into itself (but not pointwise invariant). [5] A circle not passing through O inverts to a circle not passing through O ...