Perimeter of Ellipse

[Panna Lal Patodia]

I find the following code for perimeter (or circumference of ellipse):

12*Integral(sqrt((-8*_x**2/9 + 1)/(-_x**2 + 1)), (_x, 0, 1))

This means the calculation depends on numerical integration which is very time consuming.

I am attaching a file containing Python sympy code to calculate numerical value of perimeter of ellipse to hundreds of decimal places. It computes value of

perimeter of Ellipse for 800 decimals in less than 1 second on my computer.

Please incorporate in sympy after necessary modification if you find it suitable.

Regards

Panna Lal Patodia

pann...@usa.net, panna...@gmail.com

[Panna Lal Patodia]

I am attaching a new file giving program with comments. I have also made slight changes so that if parameters are negative, it takes absolute value and computes perimeter of ellipse correctly.

[Kalevi Suominen]

This looks like a computation of the arithmetic-geometric mean (https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean). There is an implementation called agm in mpmath. You could also use that for a complete elliptic integral of the first kind.

Kalevi Suominen