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Illustration of a unit circle. The variable t is an angle measure. Animation of the act of unrolling the circumference of a unit circle, a circle with radius of 1. 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]
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 ]
Penny graphs have also been called unit coin graphs, [2] because they are the coin graphs formed from unit circles. [1] If each vertex is represented by a point at the center of its circle, then two vertices will be adjacent if and only if their distance is the minimum distance among all pairs of vertices. Therefore, penny graphs have also been ...
Because the "sweep" of the area under the involute is bounded by a tangent line (see diagram and derivation below) which is not the boundary (¯) between overlapping areas, the decomposition of the problem results in four computable areas: a half circle whose radius is the tether length (A 1); the area "swept" by the tether over an angle of 2 ...
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 ]
The circle packing theorem [2] states that every planar graph can be represented as a contact graph of circles. The contact graphs of unit circles are called penny graphs . [ 3 ] Representations as contact graphs of triangles , [ 4 ] rectangles , [ 5 ] squares , [ 6 ] line segments , [ 7 ] or circular arcs [ 8 ] have also been studied.