(There is also a
german version of this page.)
## What is it about?

In a course for high school students in the winter term
2000/01 entitled
Propädeutikum Mathematik,
we studied Steiner's beautiful result on closed chains of
circles. The statement of this theorem is quite surprising:
## Can we see this theorem »in action«?

My colleague
B. Schmitt
programmed a nice animation, which you can see below
(if your browser displays animations).
The inner circle and the outer circle are chosen in such a way
that there exists a closed chain of circles in between them.
Steiner' theorem guarantees then that we may »rotate«
this chain.
## Are there other beautiful theorems of this kind?

Sure. There are in fact plenty of such nice theorems, called
»porisms«. Have a look at
Poncelet's theorem -- in a way it is
the »prototype« of all geometric porisms.

If there is a closed chain of circles that is tangent to two given circles, then there are infinitely many such chains.

Did you notice that the circles continually change their radius when they move around? Nonetheless we can be sure that the chain remains closed at any time; it will never break apart -- that is what Steiner's result essentially says.