In mathematics, an n-sphere or hypersphere is an ⁠ ⁠ - dimensional generalization of the ⁠ ⁠ -dimensional circle and ⁠ ⁠ -dimensional sphere to any non-negative integer ⁠ ⁠.

We derive the volume of an n-sphere, using argumentation given by Weisstein [3]. We use the geometers’ nomenclature for n-sphere, n referring to the number of the underlying dimension …

Apr 8, 2025 · Geometry Multidimensional Geometry n-Dimensional Geometry Geometry Solid Geometry Spheres n-Sphere

5 days ago · The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) to …

A "sphere" of radius R in n dimensions is defined as the locus of points with a distance less than R from a given point. This implies that a sphere in n = 1 dimension is just a line segment of …

May 5, 2017 · The surface area of n-dimensional sphere of radius r is proportional to rn 1. Sn(r) = s(n)rn 1; (2) where the proportionality constant, s(n), is the surface area of the n-dimensional …

The n -sphere is the boundary of the (n + 1) - ball. These spheres, or rather their underlying topological spaces or simplicial sets, are fundamental in (ungeneralised) homotopy theory.

In mathematics, an n-sphere is a topological space that is homeomorphic to a standard n-sphere, which is the set of points in (n + 1)-dimensional Euclidean space that are situated at a …

Dec 31, 2023 · An n-sphere, denoted as S^n, is a generalization of a sphere in n-dimensional Euclidean space. It is defined as the set of all points equidistant from a center point with a …

An n-sphere is the surface or boundary of an (n + 1)-dimensional ball, and is an n-dimensional manifold. For n ≥ 2, the n-spheres are the simply connected n-dimensional manifolds of …