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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. Circle packing in a circle - Wikipedia

    en.wikipedia.org/wiki/Circle_packing_in_a_circle

    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 ]

  4. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.

  5. Goat grazing problem - Wikipedia

    en.wikipedia.org/wiki/Goat_grazing_problem

    Let be the center of a unit circle. A goat/bull/horse is tethered at point Q {\displaystyle Q} on the circumference. How long does the rope r {\displaystyle r} need to be to allow the animal to graze on exactly one half of the circle's area (white area in diagram, in plane geometry, called a lens )?

  6. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    Draw the unit circle, and let P be the point (−1, 0). A line through P (except the vertical line) is determined by its slope. Furthermore, each of the lines (except the vertical line) intersects the unit circle in exactly two points, one of which is P. This determines a function from points on the unit circle to slopes.

  7. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem. The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.

  8. Circle packing in a square - Wikipedia

    en.wikipedia.org/wiki/Circle_packing_in_a_square

    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 in order to maximize the minimal separation, d n , between points. [ 1 ]

  9. 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 ]

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