- #1

- 3

- 0

I wanted to ask about how to compute the area of a hyperboloid given in general by

(x/a)^2 + (y/b)^2 - (z/c)^2 = 1

I know this is parameterised by (acos(u)cosh(v), bsin(u)cosh(v), csinh(v))

and I used the definition that A=∫√(EG-F^2) where E,G,F are from the first fundamental form

however, I wasn't able to integrate this as it is very complicated.

I thought there might be a way of solving this by considering the area of a tiny parallelogram and then integrating it but I wasn't sure how to start that!

thanks