Albion College
Mathematics and Computer Science
Quadratic Approximations to Pi, or What if Archimedes Had Had Mathematica?
Mark Bollman

Associate Professor

Department of Mathematics and Computer Science

Albion College

Archimedes (c. 287 BCE--c. 212 BCE) used polygons inscribed within and circumscribed about a circle to approximate pi. In this talk, we will extend his work by approximating the areas of circular sectors. This is done by adjoining parabolic segments to triangular subregions of his inscribed regular polygons. While much of the mathematics would have been familiar to Archimedes, the calculations involved quickly outstrip the computational power of ancient Greece, and so Mathematica is used to facilitate calculations. The method allows us to derive recurrence relations that can be used to approximate pi more accurately.
3:10 PM
All are welcome!
Palenske 227
February 17, 2011