Session:
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Other Poster
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Paper Type:
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Poster
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Title:
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Newton Iteration-based Pi Calculation
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Meeting:
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2016 Winter Meeting: New Orleans, Louisiana |
Location:
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N/A |
Date:
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Time:
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8:00AM
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Author:
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Jason Cannon-Silber, Socrates Preparatory School
970-481-5935, nealcg@gmail.com
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Co-Author(s):
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Neal C. Gallagher, III, Maura F. Gallagher, Brandon W. Mayle, Nicolas M Fair
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Abstract:
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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)).
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Footnotes:
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* Sponsored by Neal C. Gallagher, II, Ph.D.
** Additional authors Joshua M. Fair and Samual J. Konkol, Socrates Preparatory School
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Presentation:
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Presentation1.pptx.pdf
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