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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Modified Archimedes 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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8:45AM
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Author:
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Maura F. Gallagher*, Socrates Preparatory School
970-481-5935, nealcg@gmail.com
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Co-Author(s):
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Brandon W. Mayle, Joshua C. Fair, Nicolas M. Fair, Jason Cannon-Silber
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Abstract:
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The earliest known algorithm for computing Pi is the Archimedes method**. The circumference of a circle is estimated by the perimeter of a regular polygon. The number of sides of the polygon is recursively doubled to obtain an increasingly better estimate. We propose inscribing a circle with irregular polygons whose vertices have x-coordinates that occur at regularly spaced interval. A clever application of (30-60-90) triangle geometry permits us to compute Pi to a greater accuracy than that of Archimedes for polygons with the same number of sides. A simple Java program demonstrates our results.
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Footnotes:
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* Sponsored by Neal C. Gallagher, II, Ph.D.
** Heath, T.L., The works of Archimedes (Dover edition), pp 93-98, 1953.
Additional authors Neal C. Gallagher III and Samuel J. Konkol, Socrates Preparatory School
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Presentation:
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Modified Archimedes ? Calculation.pdf
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