Year: 2024
Type: article
Abstract: 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
Authors: Hugh Riley Randall, Carolina Ilie
Institution: State University of New York at Oswego
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405874589