Line-inversion and pedal transformation in the quasi-hyperbolic plane. (English) Zbl 1399.51002
Summary: The line-inversion and pedal transformation are defined in the quasi-hyperbolic plane and certain properties of these transformations are shown with regard to analogous transformations in the Euclidean, hyperbolic, isotropic and pseudo-Euclidean plane. As it is natural to observe class curves in the quasi-hyperbolic plane, i.e. line envelopes, the construction of a tangent point on any line of the class curve obtained by the line-inversion and pedal transformation is shown.
MSC:
| 51A45 | Incidence structures embeddable into projective geometries |
| 51M15 | Geometric constructions in real or complex geometry |
| 51M99 | Real and complex geometry |
| 51N25 | Analytic geometry with other transformation groups |
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