User:Becksjuergen/New formula for the circumference of the ellipse

A new formula for calculating the circumference of the ellipse:

C = 4a ((b/a)^bex +1)^ 1/bex   for    bex=ln (2) / ln (pi/2) = 1.5349285....

or

C = 4b ((a/b)^bex +1)^1/bex     which leads to the same result.

The highest deviation of this formula is 1,54%, always in comparison to the definite circumference, calculated with the numeric integration of 15 decimal place.

This formula is interesting because it is most fundamental formula.

This formula is developed with the help of the program GeoGebra. The working-file can be found in the forum of GeoGebra under Geometrie, Kegelschnitte, Ellipse, Materialien Astroidenannäherung (at the end of the side).

If the second formula of Mr. Ramanujan https://en.wikipedia.org/wiki/Ellipse is expanded with the following appendix

0.00160934997662698...(1-((2/((a/b)^(bex) + 1))^(1/bex)^0.8)^21 for bex = ln(2)/ln(pi/2) = 1.5349285....

the max. diviations reduces to 0,0213%.