Perimeter of Ellipse

[Albert Chan]

From HP Forum Archive 21, message 5, and some optimizations, I get:

Quote:local sqrt, pi = math.sqrt, math.pi

function ellipsePerimeter(a, b) -- agm2 method
    local s = 0.5 * (a*a+b*b)
    local t = 0.25
    while true do
        local k = b - a
        local s1 = s - t*k*k
        if s == s1 then return 2*pi*s/(a+0.5*k) end
        b = sqrt(a*b)
        a = a + 0.5*k
        s = s1
        t = t + t
    end
end

Example:

lua> ellipsePerimeter(1, 2) --> 9.688448220547675
lua> ellipsePerimeter(2, 3) --> 15.86543958929059
lua> ellipsePerimeter(3, 4) --> 22.103492160709504