The Classification of the Pedal Surfaces of (1, 2) Congruences and their Construction with Mathematica 4.0
by
Sonja Gorjanc
International Society for Geometry and Graphics, Croatian Society for Constructive Geometry and Computer Graphics

In the extended Euclidean space [`(E³)] the congruences of 1st order, 2nd class have been classified according to the section with the plane at infinity. In this way eight types of these congruences have been obtained.

The properties of the pedal surfaces of such congruences with the finite pole P have been studied. For the congruences of the type I-V the pedal surfaces are 4th order, contain the absolute conic and double straight line. For the types VI-VIII pedal surfaces break up into the 3rd order surface and the plane at infinity. Basic classification is made according to the number of their real straight lines. Further classification is made according to the number and kind of singular points.

The methods of synthetic and analytic geometry have been used.

The pictures of the surfaces have been constructed with Mathematica 4.0. They are obtained by using standard pachages and make relatively sophisticated shapes easier to see. For the visualisation of synthetically obtained results the animation with Mathematica 4.0 is used.

Date received: March 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-51.