Tangent Chain to equal Circles
- Author:
- Ryan Hirst
If I have a starting circle, where is the next one?
The radius of the nth circle is , and its center is a distance from .
The sequence works for any starting position.
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The Tangent Circle Problem:
- 1. Tangent along the rim: solve for k
- 2a. Initial position: http://www.geogebratube.org/material/show/id/58360
- → 2b. Tangent chain to equal circles
- 3a. Four mutually tangent & exterior circles (Apollonius): http://www.geogebratube.org/material/show/id/58189
- 3b. Vector reduction: http://www.geogebratube.org/material/show/id/58461
- Affine Transformation http://www.geogebratube.org/material/show/id/58177
- Reflection: Line about a Circle http://www.geogebratube.org/material/show/id/58522
- Reflection: Circle about a Circle: http://www.geogebratube.org/material/show/id/58185
- Circle Inversion: Metric Space: http://www.geogebratube.org/material/show/id/60132
- Sequences 1: Formation http://www.geogebratube.org/material/show/id/58896
- Sequence 1: Formation http://www.geogebratube.org/material/show/id/59816
- Sequence 1: Iteration 1 http://www.geogebratube.org/material/show/id/59828
- Example of equivalent projections: http://www.geogebratube.org/material/show/id/65754
- Final Diagram: http://www.geogebratube.org/material/show/id/65755