Invariant Center Power and Elliptic Loci of Poncelet Triangles

Helman, Mark; Laurain, Dominique; García, Ronaldo; Reznik, Dan

doi:10.1007/s10883-021-09580-z

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Proofs that loci of certain triangle centers in over the confocal family are ellipses appear in [9,10,13,32]. A theory of locus ellipticity is slowly emerging, see [16,17]. In [11,12,28], similar geometric properties and invariants are used to cluster Poncelet triangles families.…”

Section: Related Workmentioning

confidence: 99%

The Wrought Iron Beauty of Poncelet Loci

Reznik¹

2022

Preprint

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We've built a web-based tool for the real-time interaction with loci of Poncelet triangle families. Our initial goals were to facilitate exploratory detection of geometric properties of such families. During frequent walks in my neighborhood, it appeared to me Poncelet loci shared a palette of motifs with those found in wrought iron gates at the entrance of many a residential building. As a result, I started to look at Poncelet loci aesthetically, a kind of generative art. Features were gradually added to the tool with the sole purpose of beautifying the output. Hundreds of interesting loci were subsequently collected into an online "gallery", with some further enhanced by a graphic designer. We will tour some of these byproducts here. An interesting question is if Poncelet loci could serve as the basis for future metalwork and/or architectural designs.

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Section: Related Workmentioning

confidence: 99%

The Wrought Iron Beauty of Poncelet Loci

Reznik¹

2022

Preprint

Self Cite

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“…An enduring conjecture has been that the locus of the incenter X 1 of a Poncelet triangle family can only be a conic if the pair is confocal [15].…”

Section: Straight and Nearly-straight Locimentioning

confidence: 99%