Year: 2025
Type: article
Abstract: In this paper, we present two methods to derive the formula for the volume of n-dimensional spheres in Euclidean space and analyze its asymptotic behavior as n approaches infinity using Stirling’s formula. We then establish a connection between the infinite sum of all even-dimensional spheres of radius r and the exponential function through a differential equation. Our findings highlight the decay characteristics of high-dimensional volumes and reveal a novel link between geometry and analysis. This work not only refines classical volume estimation techniques but also offers valuable insights into applications in higher-dimensional mathematics, contributing to fields such as statistical mechanics and theoretical physics.
Source: Theoretical and Natural Science
Authors: Tairan Zhong, Jayne Jiang, Tina Zhang
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410129354