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A 3-D Analog of Steiner’s Porism

Owen D. Byer and Deirdre L. Smeltzer
Mathematics Magazine
Vol. 87, No. 2 (April 2014), pp. 95-99
DOI: 10.4169/math.mag.87.2.95
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.87.2.95
Page Count: 5
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A 3-D Analog of Steiner’s Porism
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Abstract

Summary Steiner’s Porism, the classical result on chains of circles discovered by Jacob Steiner in the nineteenth century, is treasured for its beauty, for its simplicity, and as one of the great applications of inversion in the plane. In this note, we extend his result to a packing of spheres in 3-space, along with a surprising connection to regular polyhedra.

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