Original scientific paper

Pedal Surfaces of the (1,2) Congruence

Sonja Gorjanc ; Faculty of Civil Engineering, University of Zagreb, Zagreb, Croatia

Abstract

In this paper the pedal surfaces of the 1st order and 2nd class congruences are deduced by quartic inversion in projective space, using the methods of synthetic geometry. It is shown that there are the 4th order surfaces with a double line, and the constructive elaboration method is given. For one class of these surfaces the parametric equations are derived, and it is shown how they could be drawn using Mathematica. Some properties of the surfaces are proved and illustrated with the pictures drawn by Mathematica.

Keywords

(1,2) congruence; pedal surfaces of congruences; quartic inversion; 4th order surfaces with one double line; 4th order surfaces with one double line which contain absolute conic; pinch-points

Hrčak ID:

165847

URI

https://hrcak.srce.hr/165847

Publication date:

10.12.1996.

Article data in other languages: croatian

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