On the Center of Mass of the Half n-Ball

This project explores how the center of mass (COM) of a half n-ball depends on the dimension, n. We study the case of uniform density, where the COM is equivalent to the object’s centroid, or geometric center. We find a closed form solution, a sequence describing the centroid in n dimensions, which confirms the common two and three dimensional cases. Furthermore, the sequence is analytically proven to converge to zero in the limit as n approaches infinity. KEYWORDS: Mechanics; Mathematical Physics; Center of Mass; Centroid; Hyper-Geometry