Sums of Numerical Powers in Discrete Mathematics

Archimedes Sums Squares in the Sand

Abstract

In the third century BCE Archimedes made astonishing discoveries of precise areas and volumes, including the area contained within one turn of what we call an Archimedean spiral. His proof hinged on determining a closed formula for a sum of squares. Here we introduce and provide for instructors a student project based on Archimedes' original source analyzing a sum of squares, designed for courses on introductory discrete mathematics or calculus.