S^5 sphere

  • Thread starter yola
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  • #1
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What does S^5 sphere mean? How can I imagine it?
Thanks
 

Answers and Replies

  • #2
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http://en.wikipedia.org/wiki/Hypersphere" [Broken]
 
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  • #3
HallsofIvy
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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])
 
  • #4
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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])
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.
 
  • #5
mathwonk
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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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