A Fourth Century Theorem for Twenty-First Century Calculus

Abstract

SummaryThe centroid theorems of Pappus (or the Pappus–Guldin theorems, or the Guldin theorems) show deep connections between areas, arc lengths, volumes of revolution, surfaces of revolution, and centers of gravity. Because these theorems are historically important results that easily extend and imply some of the most well-known formulas in integral calculus, we argue that they should be given a more central role in calculus instruction.