AAPT Abstract Archive

Abstract Information

  Session: Other Poster
  Paper Type: Poster
  Title: Newton Iteration-based Pi Calculation
  Meeting: 2016 Winter Meeting: New Orleans, Louisiana
  Location: N/A
  Time: 8:00AM
  Author: Jason Cannon-Silber, Socrates Preparatory School
970-481-5935, nealcg@gmail.com
  Co-Author(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

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