Original scientific paper

https://doi.org/10.31896/k.24.2

Steiner's Hat: a Constant-Area Deltoid Associated with the Ellipse

Ronaldo Garcia orcid.org/0000-0001-8876-6956 ; University of Goiás, Institute of Mathematics and Statistics, Goiânia, Brazil
Dan Reznik orcid.org/0000-0002-0542-6014 ; Data Science Consulting, Rio de Janeiro, Brazil
Hellmuth Stachel orcid.org/0000-0001-5300-4978 ; Vienna University of Technology Institute of Discrete Mathematics and Geometry, Vienna, Austria
Mark Helman orcid.org/0000-0002-9110-9380 ; Rice University, Weiss School of Natural Science, Houston, USA

Abstract

The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3-cusp closed-curve which is the affine image of the Steiner Deltoid. Over all M the family has invariant area and displays an array of interesting properties.

Keywords

curve; envelope; ellipse; pedal; evolute; deltoid; Poncelet; osculating; orthologic

Hrčak ID:

248410

URI

https://hrcak.srce.hr/248410

Publication date:

27.12.2020.

Article data in other languages: croatian

Visits: 1.911 *