Ellipsoid surface area

[Albert Chan]

(05-30-2021 06:04 PM)Albert Chan Wrote:  HP-41 Module: Elliptic Functions and Orthogonal Polynomials, ellipsoid area example (page 9), using RG

From formula, S = 4*pi*RG((a*b)^2, (a*c)^2, (b*c)^2), we reverse it, for definition of RG:

Code:

#cas
RG(x,y,z)
BEGIN
    local ab, ac, bc;
    ab, ac, bc := map(sqrt, [x,y,z]);
    x, z := RFD(x,z,y); // relative to b^2
    z *= (bc-ac)*(bc+ac)*(ab-ac)*(ab+ac)/3;
    return (ab*bc/ac + (x*y-z))/2;
END;  
#end

CAS> ellipsoid_area(2,4,9)               → 283.427384268
CAS> 4*π*RG(8^2,18^2,36^2)       → 283.427384268