engleski

PEDAL CURVES OF CONICS IN PSEUDO-EUCLIDEAN PLANE

We construct pedal curves of conics in the projective model of the pseudo-Euclidean plane (further in text: PE-plane). Generally pedal curves are circular quartics, but in certain cases they are degenerated into circular cubics or even conics, as in the Euclidean plane. Since the absolute points are real and since there are more types of conics in the PE-plane, there are many types of pedal curves of conics that we can not derive in the Euclidean plane. Those are entirely circular quartics and cubics with different types of singularities in the absolute points or special cases when a pedal curve is degenerated into such type of a conic which does not exist in the Euclidean plane. In this article we show only cases specific to the PE-plane, so we do not construct cases that are analogous to the Euclidean plane.

pseudo-Euclidean plane; pedal curves; entirely circular quartic; entirely circular cubic

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