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Butterfly lines' curve in pseudo-Euclidean plane

Ema Jurkin orcid id ; 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

Puni tekst: engleski pdf 203 Kb

str. 195-202

preuzimanja: 449



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.

Ključne riječi

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

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