The YNOT formula
This formula gives an approximation for the perimeter of an ellipse.
The perimeter of an ellipse with half-axes a and b is obtained as:
4 ( ay + by)1/y
with y = ln(2)/ln(pi/2) ~ 1.534928536...(y is called the YNOT-constant)
Rewritten as a function of a and the excentricity,e, this formula becomes:
4a ( 1 + (1-eČ)y/2)1/y
This approximation formula, first proposed by Roger Maertens, makes an error of at most 0.4%.