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S^5 sphere

by yola
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yola
#1
Feb1-11, 02:44 AM
P: 17
What does S^5 sphere mean? How can I imagine it?
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torquil
#2
Feb1-11, 03:32 AM
P: 641
http://en.wikipedia.org/wiki/Hypersphere
HallsofIvy
#3
Feb1-11, 05:15 PM
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It is the subset of R5 of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1[/tex]

(The "Ball", B5, is the set of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2<= 1[/tex])

torquil
#4
Feb1-11, 05:31 PM
P: 641
S^5 sphere

Quote Quote by HallsofIvy View Post
It is the subset of R5 of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1[/tex]

(The "Ball", B5, is the set of points [itex](x_1, x_2, x_3, x_4, x_5)[/itex] such that
[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2<= 1[/tex])
No, S^5 is the unit sphere in R^6, not of R^5. It should be five-dimensional, not four-dimensional. Your B^5 is correct, though.
mathwonk
#5
Feb1-11, 06:08 PM
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you might try computing the volume of B^5 to get a first idea of what it "looks" like. and then maybe you can deduce the "area" of S^4.


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