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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 515=17, 2013.

Original scientific paper

Butterfly lines' curve in pseudo-Euclidean plane

Ema Jurkin orcid id orcid.org/0000-0002-8658-5446 ; University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Pierottijeva 6, 10000 Zagreb, Croatia
Ana Sliepčević ; University of Zagreb, Faculty of Civil Engineering, Kaˇci´ceva 26, 10000 Zagreb, Croatia

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Abstract

Up till now the validity of the Butterfly theorem has been verified in
the Euclidean, isotropic, hyperbolic and pseudo-Euclidean plane. Furthermore, it
has been shown that an infinite number of butterfly points, located on a conic, is
associated with any quadrangle inscribed into a circle.
In the present paper we study the curve formed by butterfly lines. In the Euclidean
plane this curve is always a curve of order four and class three having one
real cusp while in the pseudo-Euclidean plane it can also be a curve of order four and
class three having three real cusps or a special parabola.

Keywords

pseudo-Euclidean plane; Butterfly theorem; butterfly points’ curve; butterfly lines' curve

Hrčak ID:

104417

URI

https://hrcak.srce.hr/104417

Publication date:

27.6.2013.

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