Session:

Other Poster

Paper Type:

Poster

Title:

Newton Iterationbased Pi Calculation

Meeting:

2016 Winter Meeting: New Orleans, Louisiana 
Location:

N/A 
Date:


Time:

8:00AM

Author:

Jason CannonSilber, Socrates Preparatory School
9704815935, nealcg@gmail.com

CoAuthor(s):

Neal C. Gallagher, III, Maura F. Gallagher, Brandon W. Mayle, Nicolas M Fair

Abstract:

Detailed analysis of Newton’s method for finding a zero of sin(x) located at x = Pi, has led to our discovery of a highly efficient recursive method for computing Pi based on the convergent expression x (n+1) = x(n) + sin(xn). This recursion is derived using a geometric analysis of Newton’s method. In addition this geometric analysis proves the surprising result that for any value of x such that in the interval [Pi/2 3Pi/2] that Pi = x + arcsin(sin(x)).

Footnotes:

* Sponsored by Neal C. Gallagher, II, Ph.D.
** Additional authors Joshua M. Fair and Samual J. Konkol, Socrates Preparatory School

Presentation:

Presentation1.pptx.pdf

