24 Jun
2019
24 Jun
'19
6 p.m.
PS: What about the surface area S(a,b,c) of the ellipsoid E = E(a,b,c) having semiaxes a,b,c ??? If g(a,b), g(b,c), g(c,a) are the respective girths, aka circumcrferences of ellipses e(a,b), e(b,c), e(c,a) ... ... can we express S(a,b,c) in closed form in terms of the g( , )s ??? Nicest of all'd be if S(a,b,c)^n is a polynomial in g(a,b), g(b,c), g(c,a) for some n. Hmm, so for the sphere we'd have (4π)^3 = 2π * 2π * 2π / (π^2 / 8), so conceivably, S(a,b,c)^3 = (8/π^2) g(a,b) * g(b,c) * g(c,a) Wouldn't that be nice. —Dan I wrote: ----- Let g(a,b) denote the circumference of the ellipse (x/a)^2 + (y/b)^2 = 1. Is there an closed expression for ∂g/∂a or ∂^2g/∂a∂b ? -----