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## Main Question or Discussion Point

What does S^5 sphere mean? How can I imagine it?

Thanks

Thanks

- Thread starter yola
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What does S^5 sphere mean? How can I imagine it?

Thanks

Thanks

- #2

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http://en.wikipedia.org/wiki/Hypersphere" [Broken]

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HallsofIvy

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[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1[/tex]

(The "Ball", B

[tex]x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2<= 1[/tex])

- #4

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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}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", B^{5}, 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])

- #5

mathwonk

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