## S^5 sphere

What does S^5 sphere mean? How can I imagine it?
Thanks
 Recognitions: Gold Member Science Advisor Staff Emeritus 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 $$x_1^2+ x_2^2+ x_3^2+ x_4^2+ x_5^2<= 1$$)

## S^5 sphere

 Quote by HallsofIvy 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.
 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.