In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs...

Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. If...

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...

squares can be packed into some larger shape, often a square or circle. Square packing in a square is the problem of determining the maximum number of...

The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose...

distinct from the ideas in the circle packing theorem. The related circle packing problem deals with packing circles, possibly of different sizes, on...

to Circle Packing: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circle packing theorem...

sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions...

is the three-dimensional equivalent of the circle packing in a circle problem in two dimensions. Best packing of m>1 equal spheres in a sphere setting a...

amount n of unit circles can be packed into? More unsolved problems in mathematics Circle packing in an equilateral triangle is a packing problem in discrete...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 4 other circles in the packing (kissing...

It is also related to the densest circle packing of the plane, in which every circle is tangent to six other circles, which fill just over 90% of the area...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 5 other circles in the packing (kissing...

is p6m. If a circle is inscribed in each hexagon, the resulting figure is the densest way to arrange circles in two dimensions; its packing density is π...

system and lifting the result into three dimensions, or by using the circle packing theorem. Several extensions of the theorem are known, in which the polyhedron...

Circle packing – Field of geometry closely arranging circles on a plane Circle packing in a circle – Two-dimensional packing problem Circle packing in...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 3 other circles in the packing (kissing...

geometry of circle packings in the Euclidean plane, the ring lemma gives a lower bound on the sizes of adjacent circles in a circle packing. The lemma...

even when the locations are fixed. Circle packing in a rectangle Square packing in a square De Bruijn's theorem: packing congruent rectangular bricks of...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 5 other circles in the packing (kissing...

Colin L.; Wilks, Allan R.; Yan, Catherine H. (2003), "Apollonian circle packings: number theory", Journal of Number Theory, 100 (1): 1–45, arXiv:math...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 3 other circles in the packing (kissing...

allocations is referred to as the 'circle-packing' or 'polygon-packing'. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial...

circle packing is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles,...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 3 other circles in the packing (kissing...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 5 other circles in the packing (kissing...

set of Kleinian groups; see also Circle packing theorem. The circles of Apollonius may also denote three special circles C 1 , C 2 , C 3 {\displaystyle...

as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with four other circles in the packing (kissing...

This concept generalizes the circle packings described by the circle packing theorem, in which specified pairs of circles are tangent to each other. Although...

numbers appear in the ring lemma, used to prove connections between the circle packing theorem and conformal maps. The Fibonacci numbers are important in computational...