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  2. Unit circle - Wikipedia

    en.wikipedia.org/wiki/Unit_circle

    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.

  3. Circular uniform distribution - Wikipedia

    en.wikipedia.org/wiki/Circular_uniform_distribution

    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 ]

  4. Group of rational points on the unit circle - Wikipedia

    en.wikipedia.org/wiki/Group_of_rational_points...

    For the group on the unit circle, the appropriate subgroup is the subgroup of points of the form (w, x, 1, 0), with + =, and its identity element is (1, 0, 1, 0). The unit hyperbola group corresponds to points of form (1, 0, y, z), with =, and the identity is again (1, 0, 1, 0). (Of course, since they are subgroups of the larger group, they ...

  5. File:Unit circle angles color.svg - Wikipedia

    en.wikipedia.org/wiki/File:Unit_circle_angles...

    English: Some common angles (multiples of 30 and 45 degrees) and the corresponding sine and cosine values shown on the Unit circle. The angles (θ) are given in degrees and radians, together with the corresponding intersection point on the unit circle, (cos θ, sin θ).

  6. Unit disk - Wikipedia

    en.wikipedia.org/wiki/Unit_disk

    The open unit disk forms the set of points for the Poincaré disk model of the hyperbolic plane. Circular arcs perpendicular to the unit circle form the "lines" in this model. 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.

  7. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    The volume form ⁠ ⁠ of an ⁠ ⁠ ... ⁠-sphere is the unit circle in the Euclidean plane, ... less than 2% of the cube is filled by the sphere, so that ...

  8. Unit sphere - Wikipedia

    en.wikipedia.org/wiki/Unit_sphere

    More generally, the unit -sphere is an -sphere of unit radius in (+)-dimensional Euclidean space; the unit circle is a special case, the unit -sphere in the plane. An ( open ) unit ball is the region inside of a unit sphere, the set of points of distance less than 1 from the center.

  9. Hyperbolic geometry - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_geometry

    Therefore, in hyperbolic geometry the ratio of a circle's circumference to its radius is always strictly greater than , though it can be made arbitrarily close by selecting a small enough circle. If the Gaussian curvature of the plane is −1 then the geodesic curvature of a circle of radius r is: 1 tanh ⁡ ( r ) {\displaystyle {\frac {1 ...