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2014
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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.
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Northshield, Sam. (2014). Complex Descartes Circle Theorem. American Mathematical Monthly, 121(10), pages. http://doi.org/10.4169/amer.math.monthly.121.10.927
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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