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

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

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...

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

interiors, by making a vertex for each circle and an edge for each pair of circles that kiss. The circle packing theorem, first proved by Paul Koebe in 1936...

Two-dimensional packing problem Circle packing in an isosceles right triangle – Two-dimensional packing problem Circle packing theorem – Describes the possible tangency...

circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press. Circle packings, as studied in this...

In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic...

Tangent lines to circles Circle packing theorem, the result that every planar graph may be realized by a system of tangent circles Hexafoil, the shape...

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...

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...

R(t)={\frac {4r}{\left|\csc \left({\frac {t}{2}}\right)\right|}}} Circle packing theorem Osculating curve Osculating sphere Ghys, Étienne; Tabachnikov, Sergei;...

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...

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...

intersect each other. The circle packing theorem states that every planar graph can be represented as a contact graph of circles, known as a coin graph....

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

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...

unit disks in the plane. A circle graph is the intersection graph of a set of chords of a circle. The circle packing theorem states that planar graphs...

the plane is a unit disk graph. The Circle packing theorem states that the intersection graphs of non-crossing circles are exactly the planar graphs. Scheinerman's...

described by Tutte's theorem, may be formed by projecting such a polyhedral representation onto the plane. The Circle packing theorem states that every planar...

According to the Koebe–Andreev–Thurston circle-packing theorem, any planar graph may be represented by a packing of circular disks in the plane with disjoint...

(September 1990) pp 844–850 Automatic group Cannon–Thurston map Circle packing theorem Hyperbolic volume Hyperbolic Dehn surgery Thurston boundary Milnor–Thurston...

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

mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement...

lengths. One stronger form of the circle packing theorem, on representing planar graphs by systems of tangent circles, states that every polyhedral graph...

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,...

mathematics Does the greedy algorithm always find area-maximizing packings of more than three circles in any triangle? More unsolved problems in mathematics Gian...

formula; graph labelings; planar graphs, the four color theorem, and the circle packing theorem; near-planar graphs; and graph embedding on topological...

Closed Steiner chains are the systems of circles obtained as the circle packing theorem representation of a bipyramid. Annular Steiner chains n = 3 n =...

planar graph. Alternatively, by the circle packing theorem, any planar graph may be represented as a collection of circles, any two of which cross if and only...