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Loci of Poncelet Triangles in the General Closure Case (2108.05430v2)
Published 11 Aug 2021 in math.MG, cs.GR, cs.RO, math.AG, and math.DS
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.