Original scientific paper

Steiner Curve in a Pencil of Parabolas

Ana Sliepčević ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia
Ivana Božić ; The Polytechnic of Zagreb, Zagreb, Croatia

Abstract

Using the facts from the theory of conics, two theorems that are analogous to the theorems in triangle geometry are proved. If the pencil of parabolas is given by three lines a, b, c, it is proved that, the vertex tangents of all the parabolas in the pencil, envelop the Steiner deltoid curve δ, and the axes of all parabolas in the same pencil envelop further deltoid curve α. Furthermore, the deltoid curves are homeothetic. It is proved that all the vertices in the same pencil of parabolas are located at the 4th degree curve. The above mentioned curves are constructed and treated by synthetic methods.

Keywords

Steiner deltoid curve; Wallace-Simson line; pencil of parabolas; vertex tangent

Hrčak ID:

96181

URI

https://hrcak.srce.hr/96181

Publication date:

30.1.2013.

Article data in other languages: croatian

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