Poncelet triangles: a theory for locus ellipticity

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

doi:10.1007/s13366-021-00620-0

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Cited by 5 publications

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“…Seminal studies of loci of triangle centers over families of Poncelet triangles include [14,20,23,24]. A theory for the type of locus swept by triangle centers over the confocal Poncelet family is presented in [12].…”

Section: Related Workmentioning

confidence: 99%

Exploring the Steiner-Soddy Porism

García¹,

Gheorghe²,

Reznik³

2022

Preprint

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Section: Related Workmentioning

confidence: 99%

Exploring the Steiner-Soddy Porism

García¹,

Gheorghe²,

Reznik³

2022

Preprint

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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

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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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The Wrought Iron Beauty of Poncelet Loci

Reznik¹

2022

Lecture Notes on Data Engineering and Communications Technologies

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Poncelet triangles: a theory for locus ellipticity

Cited by 5 publications

References 16 publications

Exploring the Steiner-Soddy Porism

Exploring the Steiner-Soddy Porism

The Wrought Iron Beauty of Poncelet Loci

The Wrought Iron Beauty of Poncelet Loci

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