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# Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center. 

## Circle

A circle is a simple closed shape.

## Codimension

In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.

## Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Duncan Sommerville

Duncan MacLaren Young Sommerville (1879–1934) was a Scottish mathematician and astronomer.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Flat (geometry)

In geometry, a flat is a subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

## Hypersurface

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.

## Journal of Physics A

The Journal of Physics A: Mathematical and Theoretical is a peer-reviewed scientific journal published by IOP Publishing.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## University of Michigan

The University of Michigan (UM, U-M, U of M, or UMich), often simply referred to as Michigan, is a public research university in Ann Arbor, Michigan.

## 3-sphere

In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.

## References

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