Up: The Crosscap

Equations for the Crosscap

The restriction to the unit sphere of the following function

f(x, y, z) = ( xy, yz, (z^2 - x^2)/2 ),
defines a map from RP^2 to R^3. Parametrically, the crosscap is given by
[ (sin(u)*sin(2*v))/2, sin(2*u)*cos(v)^2, cos(2*u)*cos(v)^2 ]
0 <= u <= Pi, -Pi/2 <= v <= Pi/2

source: Gerd Fischer, ed. Mathematical Models from the Collections of Universities and Museums, Vol. 1 & 2.

Up: The Crosscap
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Created: Jun 27 1995 ---- Last modified: Wed Aug 16 20:20:47 1995
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