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 and so that no circle can be enlarged without creating an overlap.

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

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres is called a sphere packing.

Our story traces its origin to William Thurston’s famous Notes. In constructing 3-manifolds, Thurston proves that associated with any triangulation of a sphere is a “circle packing”, that is, a configuration of circles which are tangent with one another in the pattern of the triangulation.

The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in general, on …

This is a review of Introduction to Circle Packing: The Theory of Discrete Analytic Functions, by Kenneth Stephenson, Cambridge University Press, Cambridge UK, 2005, pp. i-xii, 1{356, $42, ISBN-13 978-0-521-82356-2.

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2024年7月14日 · Circle packing is a neat branch of mathematics that has led to some cool applications. It also creates an infinite set of new puzzles for ambitious mathematicians to try and solve for...

A circle packing is a configuration Pof circles realizing a specified pattern of tangencies. As such, it enjoys dual natures— combinatoric in the pattern of tangencies, encoded in an abstract “complex” K, and geometric in the radii of the circles, represented by a radius “label” R. As an early example, Fig. 1

A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to the latest theory, computations, and applications.