Steiner's Porism

Start with two fixed circles, one inside the other, but not necessarily right in the center of the other. Place a circle between and touching the two circles. Place another between and touching the two circles but also touching the circle you just placed. Repeat. Eventually, your circles will go all the way around the ring. In some instances, the last circle you placed will just touch the first circle. Steiner's Porism says that if that occurs, then it doesn't matter where you put the first circle; the last will always touch the first.

java applet or image

This figure utilizes the Geometry Applet.

March, 1996.
David E. Joyce
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610

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