Thread: Perimeter of an Ellipse

I need to know how one would evaluate this expression given:



Here's the expression for the major radius a and minor radius b of an ellipse:



Where:

Originally Posted by Aryth

I need to know how one would evaluate this expression given:



Here's the expression for the minor radius a and major radius b of an ellipse:



Where:

Here is what Wikipedia has to say about it:

Those are all approximations (With the exception of the sum/product), I'm familiar with those and I have my own approximation whose error cannot exceed:



Where e is eccentricity and for my particular case, it is:



So, the approximation is very close, yet I wish to have an exact measurement, and according to my research, this is one of four exact methods.

I was wondering how to use the series above. I'm not very experienced with infinite series, which is why I posted it.

Originally Posted by Aryth

Those are all approximations (With the exception of the sum/product), I'm familiar with those and I have my own approximation whose error cannot exceed:



Where e is eccentricity and for my particular case, it is:



So, the approximation is very close, yet I wish to have an exact measurement, and according to my research, this is one of four exact methods.

I was wondering how to use the series above. I'm not very experienced with infinite series, which is why I posted it.

It is exact untill you want to evaluate it when (except for a few special cases) you will have to used an approximation to the sum. There is no general finite closed form expression for this in terms of elementary functions

RonL