# S^5 sphere

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

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

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HallsofIvy
Homework Helper
It is the subset of R5 of points $(x_1, x_2, x_3, x_4, x_5)$ such that
$$x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1$$

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

It is the subset of R5 of points $(x_1, x_2, x_3, x_4, x_5)$ such that
$$x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2= 1$$

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

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