The Geometry Junkyard


The following set of nine circles requires five colors, if each pair of tangent circles must have distinct colors. It is an open problem, posed by Ringel, whether five or any finite number of colors is always enough for any circle arrangement (having no triple tangencies).

Five-chromatic tangent circles
If you were running Java, you'd see a nice animation instead of this gif.

Ok, I admit it, these pages are merely an excuse for me to try out Cinderella, a nice multiplatform Java application by Kortenkamp and Richter-Gebert for setting up this sort of animation. The black spots are anchor points, that you can drag around to produce different sets of circles with the same tangency pattern.

But anyway, there is some interesting math involved in constructing the circles above:


Three Tangent Circles

Four Tangent Circles

Circular Angle Bisectors

Steiner's Porism

Apollonian Circles

Many Circles

See also Paul Kunkel's tangent circles page for even more animated constructions.

From the Geometry Junkyard, computational and recreational geometry.
David Eppstein, Theory Group, ICS, UC Irvine.

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