A ruled surface of degree 4

Degree 4 ruled: Tangent surface
      of the
twisted cubic

    This figure shows a portion of a degree 4 ruled surface. It can be view as a modification of the tangent surface of a twisted cubic. Specifically, each line on the surface is a secant line of the twisted cubic -- rather than a tangent line. Each color change that occurs along a smooth part of the surface -- whether from blue to yellow, from green to pink, or from red to purple -- occurs along a straight line that lies on the surface. Two smooth sheets of the surface cross along the twisted cubic curve.

    For discussion of the relationship between this surface and the tangent surface of the twisted cubic, please click here.

  Viewing suggestions:
1.   Mouse moves in a horizontal direction are highly recommended.  This type of move will rotate the surface around the vertical axis.
2.   This figure sometimes loads slowly.   Please be patient.

The Java files used in this page were downloaded from the Geometry Center webpage.
I generated the geometric data for this figure in May 2010.
Updates completed on June 9, 2010.

Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455

Office: 531 Vincent Hall
Phone: (612) 626-9135
Dept. FAX: (612) 626-2017
e-mail: roberts@math.umn.edu