This figure shows another view of the same surface with a standard pinch point.Recall that it is given parametrically by:
(s,t) ---> (x, y, z) = (s, t2, st).
The range of values shown in the figure is -1 < s < 1
and -1 < t < 1.
In the "home position" of this sketch we are looking at the surface from
the direction of the positive y-axis,
i.e. along the singular locus.
The surface crosses itself along the positive y-axis because each point
of the positive x-axis has two pre-images
in the parametrization.
Namely, (0,t) and (0,-t) both map to
(0,t2,0). Values near t = -1 correspond
to the
light green coloring; t-values near +1
correspond to the red coloring.
Please feel free to use the mouse to rotate the surface.
Click here to return to the
other view of this surface.
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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