Newton’s Unfinished Business: Uncovering the Hidden Powers of Eleven in Pascal’s Triangle

Author(s)

Robert Arnold
Tom Attenweiler
Christopher Brockman
Bethany Lesko
Christine Martinek
Colleen McCormick
Jessica McQuiston
Jessica Parker
Amy Rohmiller

Document Type

Article

Publication Date

2004

Abstract

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle.

Disciplines

Mathematics

eCommons Citation

Arnold, Robert; Attenweiler, Tom; Brockman, Christopher; Lesko, Bethany; Martinek, Christine; McCormick, Colleen; McQuiston, Jessica; Parker, Jessica; and Rohmiller, Amy, "Newton’s Unfinished Business: Uncovering the Hidden Powers of Eleven in Pascal’s Triangle" (2004). Undergraduate Mathematics Day: Past Content. 6.
https://ecommons.udayton.edu/mth_epumd/6