The window "Domain" displays a domain, a point (u0,
v0) in the domain, a subset of the domain colored red,
yellow, cyan, and blue, and a point on the boundary of this subset.
The window "Surface" shows the surface X(u, v) = (u cos(v), u sin(v), ln(u)),
the image of (u0, v0) and the colored subset of
the domain on this
surface (with each point in the domain mapped to a point of the same
color), and the normal vector to X(u, v) at X(u0, v0).
The window "Area
Element" shows the graph of the integrand √(g11(u,v)g22(u,v)
– g12(u,v)2), which, when integrated,
gives the area of
It is possible
to drag the two points shown in the "Domain" window to change (u0,
and the colored subset of the domain.