S^5 sphere

yola

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

torquil

http://en.wikipedia.org/wiki/Hypersphere

HallsofIvy

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

Quote by HallsofIvy

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

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

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	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])

mathwonk Recognitions: Homework Help Science Advisor	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.