Viète’s Formula, Knar’s Formula, and the Geometry of the Gamma Function

Abstract

The gamma function was originally discovered by Euler to solve an interpolation problem for the factorials. However, its ubiquity cannot be due to its algebraic nature alone. This article presents the close connection between the volumes of various spaces and the values of the gamma function to better understand its frequent appearance in many mathematical formulas. This connection produces a surprising similarity between Viète’s formula for π and Knar’s formula.

Key words:

• MSC: Primary 33B15

Acknowledgment

The author thanks Sabine Bucheister for her excellent detective skills and invaluable help tracking down and translating the original references for Joseph Knar and his formula.

Additional information

Notes on contributors

John Pearson

John Pearson received his Ph.D. from Georgia Tech in 2008. His thesis, studying the noncommutative geometry of Cantor sets, won the Department’s Best Thesis Award. A passion for teaching in a close-knit community led him to Pace Academy where he has had the chance to work with gifted students and research in his spare time.