## Tangent surface of the twisted cubic

 Tangent surface       of the twisted cubic: Introduction Equal   segments Implicit   equation Static figure   (Visit this link if the figure won't load.) Tangent surface of a rational curve of degree 4: Other: View with equal segment lengths:       This 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.     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 the point of tangency on 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. Viewing suggestions:      I recommend long diagonal mouse motions. (Upper left to lower right, for instance.)

Updates completed on July 14, 2010.

Prof. Joel Roberts
School of Mathematics
University of Minnesota
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USA

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e-mail: roberts@math.umn.edu
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