Area-invariant pedal-like curves derived from the ellipse

Reznik, Dan; García, Ronaldo; Stachel, Hellmuth

doi:10.1007/s13366-021-00588-x

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Other1

Article1

Relationship

Self Cite1

Independent1

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…derivatives [22]. We have also studied the locus of Brocard points over circle-and ellipse-inscribe triangle families [6].…”

Section: Introductionmentioning

confidence: 99%

Intriguing Invariants of Centers of Ellipse-Inscribed Triangles

Helman,

Garcia,

Reznik

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We study a family of ellipse-inscribed triangles with two vertices V 1 , V 2 fixed on the ellipse boundary while a third one which sweeps it. We prove that: (i) if a triangle center is a fixed linear combination of barycenter and orthocenter, its locus over the family is an ellipse; (ii) over the 1d family of said linear combinations, loci centers sweep a line; (iii) over the family of parallel V 1 V 2 , said elliptic loci are rigidly-translating ellipses. Additionally, we study the external envelope of elliptic loci for fixed V 1 and over all V 2 on the ellipse. We show that (iv) the area of said envelope is invariant with respect to V 1 , and that (v) for the barycenter (resp. orthocenter), the envelope is an ellipse (resp. an affine image of Pascal's Limaçon).

show abstract

“…derivatives [22]. We have also studied the locus of Brocard points over circle-and ellipse-inscribe triangle families [6].…”

Section: Introductionmentioning

confidence: 99%