Steiner's Chain: What is it?
A Mathematical Droodle

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The applet offers one illustration of Jacob Steiner's wonderful theorem that says that, for two concentric circles, either there exists a closed chain of circles tangent to the given two as well as to their immediate neighbors in the chain, or such a chain does not exist. In the former case, the chain could be started at the arbitrary location in the ring between the two circles.

A transparent proof makes use of the inversion transform.

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Steiner's Chain: What is it? A Mathematical Droodle

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

Steiner's Chain: What is it?
A Mathematical Droodle