Original scientific paper

Special sextics with a quadruple line

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

Abstract

This paper deals with a special class of 6th order surfaces with a quadruple straight line in a three-dimensional Euclidean space. These surfaces, denoted by $\mathcal P_4^6$, are the pedal surfaces of one special 1st order 4th class congruence $\mathcal C_4^1$. The parametric and implicit equations of $\mathcal P_4^6$ are derived, some of their properties are proved and their visualizations are given. The singularities of $\mathcal P_4^6$ are classified according to the shapes of their tangent cones. The methods applied are analytic, synthetic and algebraic, supported by the program Mathematica 6.

Keywords

congruence of lines; pedal surface; multiple point; pinch-point; tangent cone

Hrčak ID:

37361

URI

https://hrcak.srce.hr/37361

Publication date:

3.6.2009.

Visits: 1.164 *