Complex Descartes Circle Theorem
We present a short proof of Descartes Circle Theorem on the curvature-centers of four mutually tangent circles. Key to the proof is associating an octahedral configuration of spheres to four mutually tangent circles. We also prove an analogue for spheres.
This article has been published in the December 2014 issue of American Mathematical Monthly, published by Taylor & Francis, Ltd. on behalf of the Mathematical Association of America: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.10.927