engleski

Butterfly Curve Theorems in pseudo-Euclidean Plane

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.

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

Rad je kao predavanje prezentiran na skupu Mathematics in Architecture and Civil Engineering, Design and Education, održanom od 06.-28.05.2011., Pečuh, Mađarska ; uz međunarodnu recenziju objavljen u Knjizi sažetaka.