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Steiner Curve in a Pencil of Parabolas

Ana Sliepčević ; Građevinski fakultet Sveučilišta u Zagrebu, Zagreb, Hrvatska
Ivana Božić ; Tehničko veleučilište u Zagrebu, Zagreb, Hrvatska

Sažetak

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.

Ključne riječi

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

Hrčak ID:

96181

URI

https://hrcak.srce.hr/96181

Datum izdavanja:

30.1.2013.

Podaci na drugim jezicima: hrvatski

Posjeta: 1.673 *