From the start, I was never entirely sold on the idea of Chat Circles. I very much liked how the user's avatar was a circle on the visualization plane, and how it changed to match the users activity. However, immediately my concern turned to people abusing this fact. From the looks of the prototype pictures, players chat will be displayed inside their circle. What is to stop a user from spammin...

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G there corresponds a circle. If two vertices are connected by an edge in G then the corresponding circles intersect with an intersection angle in (0, π) and these intersection points can be associated to the dual graph G. Two sequences of circle patterns are ...

| According to a remarkable re-interpretation of a theorem of E.M. Andreev (1970) by W.P. Thurston (1982), there is a unique (up to inversive transformations) packing of interior-disjoint circles in the plane, whose contact graph is any given polyhedral graph G, and such that an analagous \dual" circle packing simultaneously exists, whose contact graph is the planar dual graph G , and such that...

Equations are developed for the potential due to a source and sink, or dipole, inside a circle of finite resistivity surrounded by a two-dimensional infinite medium of different resistivity. When the resistivity of the external medium is allowed to increase to infinity, the resulting equations give identical results to those presented by Bayley for the dipole potential in an insulating circle. ...

We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe–Thurston–Andreev circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Möbius transformations, defined using three-dimensional hyp...