The window "Domain" displays a domain as a
wireframe, a point (u_{0}, v_{0}) in the domain, and
the u-constant and
v-constant curves through that point in red and green, respectively.

The window "Surface X(u,v)" shows the Möbius strip X(u,v) = ((2 –
vcos(u/2))cos(u), (2 – vcos(u/2))sin(u), vsin(u/2)) for
the
given domain, the images of the point and the curves from the
"Domain" window, the tangent vectors X_{u}(u_{0},v_{0})
and X_{v}(u_{0},v_{0}) to the
surface at the point X(u_{0},v_{0}), and the unit
normal
vector

N(u_{0},v_{0}) = (X_{u}(u_{0},v_{0})
× X_{v}(u_{0},v_{0}))/|X_{u}(u_{0},v_{0})
× X_{v}(u_{0},v_{0})|
to the
surface at the point X(u_{0},v_{0}).

Checking the "Show
tangent plane" checkbox will show the tangent plane to X(u,v) at the
point
X(u_{0},v_{0}). (Note that this box is checked by
default.) It is possible to change u_{0}
and v_{0} in the control window.