I've been researching for the calculus behind geodesic domes, and specifically calculus related to parametric surfaces. I've found this, but unfortunately it comes short of providing me the most needed information, and so far I couldn't find the information anywhere else.
Basically, Yale says,
For a surface defined parametrically by x = x(u, v), y = y(u, v), and z = z(u, v), the geodesic can be found by minimizing the arc length
(formulas available in print form) ...
For a surface of revolution in which y = g(x) and is rotated about the x-axis so that t
(formulas available in print form)
Could someone please help me figure out what these "formulas available in print form" are? Thank you so much in advance.