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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. Group of rational points on the unit circle - Wikipedia

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

    The Pythagorean triple (4,3,5) is associated to the rational point (4/5,3/5) on the unit circle. In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x 2 + y 2 = 1. The set of such points turns out to be closely related to primitive Pythagorean triples.

  4. Circle group - Wikipedia

    en.wikipedia.org/wiki/Circle_group

    Moreover, since the unit circle is a closed subset of the complex plane, the circle group is a closed subgroup of (itself regarded as a topological group). One can say even more. The circle is a 1-dimensional real manifold , and multiplication and inversion are real-analytic maps on the circle.

  5. Poincaré disk model - Wikipedia

    en.wikipedia.org/wiki/Poincaré_disk_model

    Poincaré disk with hyperbolic parallel lines Poincaré disk model of the truncated triheptagonal tiling.. In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or ...

  6. Smallest-circle problem - Wikipedia

    en.wikipedia.org/wiki/Smallest-circle_problem

    The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.

  7. Unit sphere - Wikipedia

    en.wikipedia.org/wiki/Unit_sphere

    In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. More generally, the unit n {\displaystyle n} -sphere is an n {\displaystyle n} -sphere of unit radius in ( n + 1 ) {\displaystyle (n+1)} - dimensional Euclidean space ; the unit circle is a ...

  8. 3-sphere - Wikipedia

    en.wikipedia.org/wiki/3-sphere

    Under this map all points of the circle of radius π are sent to the north pole. Since the open unit disk is homeomorphic to the Euclidean plane, this is again a one-point compactification. The exponential map for 3-sphere is similarly constructed; it may also be discussed using the fact that the 3-sphere is the Lie group of unit quaternions.

  9. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter.