# Ruslan and Ludmila

Author:
Ryan Hirst
A couple of simple thoughts. Push Naina around. Finn is afraid of her.
________________ What interests me most about the pole/polar relationship is how a free point can be bound very tightly by crossing a boundary, without changing its definition on that boundary. Move Finn until Ludmila falls in his circle. He wraps her up. Here, in addition, if Ruslan, Ludmila or Chernomor go inside Finn's circle, the polar relationship is expressed incorrectly(mathematically). The polar is drawn as a tangent. I like the way this behaves. I will add the condition that, say, if Chernomor no longer can control Ludmila if he does not intercept her polar, then she can get off his line by entering the circle, or getting him into it. Likewise, with all the actors outside the circle, whenever Ruslan's line intersects Ludmila, he he, too falls on Chernomor's line. Inside the circle, the bind is broken. Looking for smooth transitions for boundaries, envelopes, boolean conditions. ___ Pole and Polar: 1. Basic construction: http://www.geogebratube.org/material/show/id/34578 2. Reduced Construction (& Vectors): http://www.geogebratube.org/material/show/id/34585 →3. Ruslan and Ludmila Fin.