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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.
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:
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 aiming to get the greatest minimal separation, d n, between points. [1]
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 ]
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 )?
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 ]
Another convex set whose opaque sets are commonly studied is the unit circle, for which the shortest connected opaque set has length +. Without the assumption of connectivity, the shortest opaque set for the circle has length at least π {\displaystyle \pi } and at most 4.7998 {\displaystyle 4.7998} .
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.