AAPT Abstract Archive

Abstract Information

  Session: Other Poster
  Paper Type: Poster
  Title: Modified Archimedes Pi Calculation
  Meeting: 2016 Winter Meeting: New Orleans, Louisiana
  Location: N/A
  Time: 8:45AM
  Author: Maura F. Gallagher*, Socrates Preparatory School
970-481-5935, nealcg@gmail.com
  Co-Author(s): Brandon W. Mayle, Joshua C. Fair, Nicolas M. Fair, Jason Cannon-Silber
  Abstract: 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.
  Footnotes: * 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
  Presentation: Modified Archimedes ? Calculation.pdf

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