Circles on the Rim, 3: Iteration

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. _________________ The Tangent Circle Problem: [list] [*]1. Tangent along the rim: solve for k [*]2a. Initial position: [url][/url] [*]2b. Tangent to equal circles: [url][/url] [*]3a. Four mutually tangent & exterior circles (Apollonius): [url] [/url] [*]3b. Vector reduction: [url][/url] [/list] [list] [*]Affine Transformation [url][/url] [*]Reflection: Line about a Circle [url][/url] [*]Reflection: Circle about a Circle: [url][/url] [*]Circle Inversion: Metric Space: [url][/url] [/list] Solution: [list] [*]Sequences 1: Formation [url][/url] [*]Sequence 1: Formation [url][/url] [*][b]→Sequence 1: Iteration 1[/b] [*]Example of equivalent projections: [url][/url] [*]Final Diagram: [url][/url] [/list]


Ryan Hirst

Resource Type
circle  conic  conic-sections  projection  sections  tangency 
Target Group (Age)
English (United States)
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