![]() By using my formula, the pi number can be created by hand easily. The BBP formula was created by complicated function, and also we can’t use the formula easily.Īpologise, as I posted on, after a week from the last Pi Day (3/14/09) I found a simple analytic exact formula for pi number that now in preparing to be published. Recently, creating the pi number until more than million digits has been performed using BBP Formula based on haxadecimal coding, please visit to this link for detail explanation, But, there is still problem because the formula contains the arctan function. The simpliest exact formula of pi is 4*arctan(1), where arctan(1)=1-1/3+1/5-1/7+1/9… But as discussed here, the primary drawback of the infinite series of 1-1/3+1/5-1/7+1/9…called as Gregory-Leibniz Series is too slowly to converg, that also shown on this link :Īctually, there is another exact formula or the pi number called Machin’s Formula We know that until now there are so many formulas for pi number. Oh thanks, you are pleased me to give brief explanation about the simple analytical formulation for pi number. View all posts by Autar Kaw Author Autar Kaw Posted on Categories Numerical Methods Tags gregory series pi, matlab, ramanajun series pi He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. The OpenCourseWare (nm.) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. in Engineering Mechanics from Clemson University. He has been at USF since 1987, the same year in which he received his Ph. Let the information follow you.Īutar Kaw () is a Professor of Mechanical Engineering at the University of South Florida. Subscribe to the blog via a reader or email to stay updated with this blog. Īn abridged (for low cost) book on Numerical Methods with Applications will be in print (includes problem sets, TOC, index) on Decemand available at lulu storefront. This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at. Legend(‘Gregory Series’,’Ramanajun Series’,1) Plot(x,pi_ram_array,’color’,’black’,’LineWidth’,2) Plot(x,pi_gregory_array,’color’,’blue’,’LineWidth’,2) ![]() Title(‘Comparing Gregory and Ramanujan series’) %% PLOTTING THE TWO SERIES AS A FUNCTION OF TERMS %If you want to experiment this the only parameter % pi using a) Gregory series and b) Ramanajun seriesĭisp(‘This program compares results for the value of’)ĭisp(‘pi using a) Gregory series and b) Ramanajun series’)ĭisp(‘pi=sum over k from 0 to inf of (4*((-1)^k/(2*k+1))’)ĭisp(‘1/pi=sum over k from 0 to infinity of 2*sqrt(2)/9801*((4k)!*(1103+26390k)/(k!)^4*396^(4*k))’) ![]() % Abstract: This program compares results for the value of The html file showing the mfile and the command window output is also available. The MATLAB program can be downloaded as a Mfile (better to download it, as single quotes from the web-post do not translate correctly with the MATLAB editor). Here is a MATLAB program that does the comparison for you. In this blog, we compare two series, one by Gregory and another by Ramanujan. Many series are used to calculate the value of pi.
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