Session:

Other Poster

Paper Type:

Poster

Title:

Modified Archimedes Pi Calculation

Meeting:

2016 Winter Meeting: New Orleans, Louisiana 
Location:

N/A 
Date:


Time:

8:45AM

Author:

Maura F. Gallagher*, Socrates Preparatory School
9704815935, nealcg@gmail.com

CoAuthor(s):

Brandon W. Mayle, Joshua C. Fair, Nicolas M. Fair, Jason CannonSilber

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 xcoordinates that occur at regularly spaced interval. A clever application of (306090) 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 9398, 1953.
Additional authors Neal C. Gallagher III and Samuel J. Konkol, Socrates Preparatory School

Presentation:

Modified Archimedes ? Calculation.pdf

