engleski

Butterfly Lines' Curve in pseudo-Euclidean Plane

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.

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

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