Loci of Poncelet Triangles in the General Closure Case
arXiv:2108.05430
Abstract
We analyze loci of triangle centers over variants of two-well known triangle porisms: the bicentric and confocal families. Specifically, we evoke the general version of Poncelet's closure theorem whereby individual sides can be made tangent to separate in-pencil caustics. We show that despite the more complicated dynamic geometry, the locus of certain triangle centers and associated points remain conics and/or circles.
24 pages, 18 figures, 4 tables, 18 video links