2006-12-06 23:37:41 · 11 answers · asked by BARROWMAN 6 in Science & Mathematics ➔ Mathematics
Hypersphere: 4 dimiensional and beyond
Another sequence is point, line, square, cube, hypercube .
2006-12-06 23:42:00 · answer #1 · answered by albert 5 · 1⤊ 0⤋
There is a very real geometric object, realizable within the relativistic geometry of our universe, which has the properties of a sphere in four dimensions (a "4-hypersphere").
A circle (or: a "hypersphere in two dimensions") is the locus of points on a plane (2D-space) that have the same distance from a fixed center.
A sphere (or: a "hypersphere in three dimensions") is the locus of points in the 3D-space that have the same distance from a fixed center.
Therefore, by analogy it follows that a 4D-sphere (or: a "hypersphere in four dimensions") has to be the locus of points in the 4D-space that have the same distance from a fixed center.
I hope that is clear.
All the best.
2006-12-07 08:34:32 · answer #2 · answered by Paritosh Vasava 3 · 0⤊ 0⤋
A 3-sphere (which is a particular form of the hypersphere).
This is the locus of all points in 4 dimensions that are a given distance from the origin.
2006-12-07 14:13:22 · answer #3 · answered by waspy772004 3 · 0⤊ 0⤋
4D => A sphere at a certain time.
2006-12-07 10:10:00 · answer #4 · answered by Kemmy 6 · 0⤊ 0⤋
Point
2006-12-07 07:50:55 · answer #5 · answered by Anonymous · 0⤊ 1⤋
4-dimensional hypersphere.
2006-12-07 07:50:48 · answer #6 · answered by ddntruong 2 · 0⤊ 0⤋
moving sphere.
You're adding in a dimension at each stage
2006-12-07 07:46:41 · answer #7 · answered by Michael H 7 · 0⤊ 0⤋
3-dimensional ball
2006-12-07 07:59:12 · answer #8 · answered by mynah bird 1 · 0⤊ 1⤋
oblate spheroid ?
2006-12-07 07:39:17 · answer #9 · answered by Well, said Alberto 6 · 0⤊ 0⤋
hypersphere
1D, 2D, 3D, ... 4D
2006-12-07 07:39:43 · answer #10 · answered by anton3s 3 · 0⤊ 0⤋