In geometry, circlepacking is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs...
The circlepacking theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circlesin the plane whose...
squares can be packed into some larger shape, often a square or circle. Square packingina square is the problem of determining the maximum number of unit...
three-dimensional equivalent of the circlepackinginacircle problem in two dimensions. Best packing of m>1 equal spheres ina sphere setting a new density record...
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...
In mathematics, a Ford circle is acirclein the Euclidean plane, ina family of circles that are all tangent to the x {\displaystyle x} -axis at rational...
An osculating circle is acircle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has...
In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. If the arbelos...
Integral Apollonian circlepacking defined by circle curvatures of (−3, 5, 8, 8) Integral Apollonian circlepacking defined by circle curvatures of (−12...
to CirclePacking: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circlepacking theorem...
have been packing stones used to support the larger stones when the circle was constructed and would originally have been buried. Differences in opinion...
is a generalization of Apollonius' problem, whereas Soddy's hexlet is a generalization of a Steiner chain. Tangent lines to circlesCirclepacking theorem...
An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space. Commonly, designs are...
sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circlepackingin two dimensions...
in mathematics: Does the greedy algorithm always find area-maximizing packings of more than three circlesin any triangle? (more unsolved problems in...
seen as a source of that ice and meat packing moved across the line, creating processing plants and ice house. Gary is on both routes of the Circle Tour...
equivalent of the circlepackingina square problem in two dimensions. The problem consists of determining the optimal packing of a given number of spheres...
Circlepackingina right isosceles triangle is apacking problem where the objective is to pack n unit circles into the smallest possible isosceles right...
In the mathematics of circlepacking, a Doyle spiral is a pattern of non-crossing circlesin the plane in which each circle is surrounded by a ring of...
allows for one circle, creating the densest packing from the triangular tiling, with each circlein contact with a maximum of 6 circles. There are 2 regular...
double lattice packing shown. Ina preprint released in 2016, Thomas Hales and Wöden Kusner announced a proof that this double lattice packing of the regular...
corresponding circlesin this circlepacking. Every convex polyhedron has a combinatorially equivalent polyhedron, the canonical polyhedron, that does have a midsphere...
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circlesina plane (Figure 1). Apollonius of...
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