Drawing Steiner's Chain
Take 2 circles one inside the other. (The black and green ones in the graphic)Fill it with a chain of sequentially tangential circles.(the blue ones in the graphic) If the first and last are tangential you have made a Steiner Chain. If you can fill a particular circle pair starting at one spot you can from any starting spot. If you can't do a tangential fill from a particular starting spot , you can't do it from any spot. This is Steiner's Porism. Why? Every example of the Chain maps to a simple structure based on concentric cicles. The mapping is known as a "Geometric Inversion" Everything at the center of a "circle of inversion" is moved to infinity and everything at infinity is moved to the center. Things on the circumference stay where they are.
SHOW original wheel
SHOW or HIDE the concentric structure and the "circle of inversion" used to generate the Chain
HIDE inverted wheel
SHOW or HIDE the inverted Wheel/Chain
STOP or START the continuous rotation. I enjoy the way the inversion reverses the direction of rotation.
Rotate by 1 degree
make new wheel
Make a new wheel with the entered number of circles. Try fractions (ie 5.8)
Wikipedia article on Steiner Chain
Mathworld article on Steiner's Porism
Mathworld article on Steiner Chain
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