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...

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...

shape, often a square or circle. Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one)...

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...

the ideas in the circle packing theorem. The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for...

equivalent of the circle packing in a square problem in two dimensions. The problem consists of determining the optimal packing of a given number of spheres...

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 new density record...

circle packing in a square. Packing squares into other shapes can have high computational complexity: testing whether a given number of unit squares can...

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

The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are...

Circle packing problem Tarski's circle-squaring problem – Problem of cutting and reassembling a disk into a square Thales' theorem Circle tangents in...

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...

{\displaystyle C=2} in spherical geometry and C = − 2 {\displaystyle C=-2} in hyperbolic geometry. Circle packing in a circle Euler's four-square identity Malfatti...

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...

Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points...

hexagon, the resulting figure is the densest way to arrange circles in two dimensions; its packing density is π 2 3 ≈ 0.907 {\textstyle {\frac {\pi }{2{\sqrt...

methods using the circle packing theorem to generate a canonical polyhedron. Although Steinitz's original proof was not expressed in terms of graph theory...

In geometry, Coxeter's loxodromic sequence of tangent circles is an infinite sequence of circles arranged so that any four consecutive circles in the...

2-dimensional analog of Kepler's conjecture: the regular hexagonal packing is the densest circle packing in the plane (1890). This disambiguation page lists mathematics...

corresponding circles in this circle packing. Every convex polyhedron has a combinatorially equivalent polyhedron, the canonical polyhedron, that does have a midsphere...

called a demiregular tiling by some authors. This 2-uniform tiling can be used as a circle packing. Cyan circles are in contact with 3 other circles (1 cyan...

In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of...

In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the x {\displaystyle x} -axis at rational...

highest packing density of any curve of constant width. Any curve of constant width can form a rotor within a square, a shape that can perform a complete...

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...

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...

double lattice packing shown. In a preprint released in 2016, Thomas Hales and Wöden Kusner announced a proof that this double lattice packing of the regular...

arbitrary shifts in the square row colorings. The elongated triangular tiling can be used as a circle packing, placing equal diameter circles at the center...

used as a circle packings. In the first 2-uniform tiling (whose dual resembles a key-lock pattern): cyan circles are in contact with 5 other circles (3 cyan...

surrounding squares and triangles with dodecagons: The rhombitrihexagonal tiling can be used as a circle packing, placing equal diameter circles at the center...