Up till now the validity of the Butterfly theorem has been verified in the Euclidean isotropic, and hyperbolic plane. In the present paper we prove that the Butterfly theorem also holds in the pseudo-Euclidean plane. Furthermore, it is shown that an infinite number of butterfly points, located on a conic, is associated with any quadrangle inscribed into a circle. In the Euclidean plane this conic is always a rectangular hyperbola while in the pseudo-Euclidean plane it can also be an ellipse or a special parabola. |
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