The Ballet of Triangle Centers on the Elliptic Billiard
arXiv:2002.00001
Abstract
The dynamic geometry of the family of 3-periodics in the Elliptic Billiard is mystifying. Besides conserving perimeter and the ratio of inradius-to-circumradius, it has a stationary point. Furthermore, its triangle centers sweep out mesmerizing loci including ellipses, quartics, circles, and a slew of other more complex curves. Here we explore a bevy of new phenomena relating to (i) the shape of 3-periodics and (ii) the kinematics of certain Triangle Centers constrained to the Billiard boundary, specifically the non-monotonic motion some can display with respect to 3-periodics. Hypnotizing is the joint motion of two such non-monotonic Centers, whose many stops-and-gos are akin to a Ballet.
22 pages, 16 figures, 3 tables, 15 videos. arXiv admin note: substantial text overlap with arXiv:2001.08041
References in corpus (1)
Cited by in corpus (5)
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- The number of perpendicularly inscribed polygons that intersect a given side in an odd sided regular polygon
- An App for the Discovery of Properties of Poncelet Triangles