Loci of Poncelet Triangles in the General Closure Case
This work addresses a theoretical geometry problem for mathematicians, but it appears incremental as it extends known results to a more general case.
The paper tackled the problem of analyzing loci of triangle centers in generalized Poncelet triangle porisms, showing that despite increased geometric complexity, these loci remain conics or circles.
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.