Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Ellipse circumference formula-better than Ramanujan II
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
thomasinventions@yahoo.com

Posts: 35
Registered: 12/23/11
Ellipse circumference formula-better than Ramanujan II
Posted: Jan 18, 2013 12:50 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

A formula I just came up with today is simplistic, having a maximum relative error an entire magnitude lower than Ramanujan's second formula:

C~a*[((1-sqrt(2)/2) + (sqrt(2)/2) * (b/a)^(-0.454))^(2-2pi)](2pi-4)-4
Maximum absolute relative error: ~3.8E-5 (~3.4E-5 with -0.454012 as inner power) Note: b<>0


The above could be written as the following to see the direct decomposition into the elliptical integral of the second kind (C=4aE(1-x^2)):

C~4a[1+(pi/2-1)/(((1-sqrt(2)/2)+(sqrt(2)/2)*(b/a)^(-0.454))^(2pi-2))]


I will continue on my quest to make even more dramatic improvements.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.