Appolonius' Tangency Problem: [i]To draw a circle which is tangent to three given circles.[/i] D, D2, D3 each seek the nearest tangent point according to a simple differential model: [url]http://www.geogebratube.org/material/show/id/34821[/url]
[b]To Do:[/b] Stabilize the system. Points can get trapped. Weight the forces relatively, according to the radii. Currently, angular velocity is by default equal across the circles, which causes problems. Consider adding impulses. What about tension: if two distances to tangent approach zero, while a third remains large, how should this bias be resolved? ___________ This is problem #32 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics[/i]: [list=1] [*]Geometric Solution: [url]http://www.geogebratube.org/material/show/id/34645[/url] [*]Differential Solution: a. Seek model (one circle): [url]http://www.geogebratube.org/material/show/id/34821[/url] [b]→b. Solution, v.1 [/b] c. Solution v.2, improved: [url]http://www.geogebratube.org/material/show/id/35386[/url] [/list]