Iterating on the rim.
To iterate, I could reproject the starting figure to a problem which is already solved.
But of course I could also back up and treat the whole problem as "intersect conics with circle centers as common foci," in which case the problem is solved before I started.
I would like slightly more than this. I want iteration rules, either in the original figure, or in a single projection space.
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The Tangent Circle Problem:
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[*]1. Tangent along the rim: solve for k
[*]2a. Initial position: [url]http://www.geogebratube.org/material/show/id/58360[/url]
[*]2b. Tangent to equal circles: [url]http://www.geogebratube.org/material/show/id/58455[/url]
[*]3a. Four mutually tangent & exterior circles (Apollonius): [url]http://www.geogebratube.org/material/show/id/58189 [/url]
[*]3b. Vector reduction: [url]http://www.geogebratube.org/material/show/id/58461[/url]
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[*]Affine Transformation [url]http://www.geogebratube.org/material/show/id/58177[/url]
[*]Reflection: Line about a Circle [url]http://www.geogebratube.org/material/show/id/58522[/url]
[*]Reflection: Circle about a Circle: [url]http://www.geogebratube.org/material/show/id/58185[/url]
[*]Circle Inversion: Metric Space: [url]http://www.geogebratube.org/material/show/id/60132[/url]
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Solution:
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[*]Sequences 1: Formation [url]http://www.geogebratube.org/material/show/id/58896[/url]
[*]Sequence 1: Formation [url]http://www.geogebratube.org/material/show/id/59816[/url]
[*][b]→Sequence 1: Iteration 1[/b]
[*]Example of equivalent projections: [url]http://www.geogebratube.org/material/show/id/65754[/url]
[*]Final Diagram: [url]http://www.geogebratube.org/material/show/id/65755[/url]
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