Tangent surface of the twisted cubic (equal length segments)

Tangent surface of the twisted cubic

The figure shows the tangent surface of the twisted cubic. This surface is the union of the tangent lines of the twisted cubic curve. The curve is given parametrically by: t ---> (x,y,z) = (t, t², t³), so that the surface is parametrically by:

(t,u) --> (t+u, t² + 2tu, t³ + 3t²u).

The twisted cubic curve is lightly sketched in dark blue on the surface.

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Long diagonal mouse motions are recommended. (Upper left to lower right, for instance.)

In the portion shown here, we have -1 < t < 1, while the range of u-values varies with t in such a way that a tangent line segment of length = 2 is shown for each value of t. The midpoint of each tangent line segment is at a point of the twisted cubic curve.

Return to the first view of the tangent surface of the twisted cubic.

Click here to see yet another view of the tangent surface of the twisted cubic.

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I made the figure on this page by substituting my own data in a Geometry Center webpage.

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

Office: 351 Vincent Hall
Phone: (612) 625-1076
Dept. FAX: (612) 626-2017
e-mail: roberts@math.umn.edu http://www.math.umn.edu/~roberts