3-sphere
3-dimensional compact manifold, defined as the points of unit norm in Euclidean 4-space
Nº Q2274197 ★
Common · Knowledge
3-sphere
3-dimensional compact manifold, defined as the points of unit norm in Euclidean 4-space
In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point. The interior of a 3-sphere is a 4-ball.
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From Wikipedia
In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point. The interior of a 3-sphere is a 4-ball. It is called a 3-sphere because topologically, the surface itself is 3-dimensional, even though it is curved into the 4th dimension. For example, when traveling on a 3-sphere, you can go north and south, east and west, or along a 3rd set of cardinal directions. This means that a 3-sphere is an example of a 3-manifold.
Text: Wikipédia, CC BY-SA 4.0. · Image: "Eugene Antipov" (CC BY-SA 3.0) ·
