| > Now that the arc length of an ellipse is known...
In general, the arc length of the smooth continuous single-valued function
y=y(x) is given by
/
|sqrt(1+(dy/dx)^2) dx
/
> what is the surface area on an n-dimensional ellipsoid with axes
> a1, a2, ..., an?
... and for the area of the surface z = z(x,y) it's
//
||sqrt(1+(dz/dx)^2+(dz/dy)^2) dy dx
//
and I think this generalizes easily to n dimensions.
> Can you give an accurate numerical algorithm?
Not offhand! although any good numerical integrator should do... For
ellipsoids it's probably necessary to use a parametric form
{x=x(t), y=y(t), z=z(t)} since the derivatives dy/dx etc. are infinite at
the endpoints.
|