- #1

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1) Are there surfaces (parametrized by 2 free variables), that are possible in R^4, but not in R^3 ?

2) Are there differences between the 2 following parametrizations of the 3-sphere :

w=cos(a)sin(b)

x=sin(a)sin(b)

y=cos(c)cos(b)

z=sin(c)cos(b)

w'=cos(a')

x'=sin(a')cos(b')

y'=sin(a')sin(b')cos(c')

z'=sin(a')sin(b')sin(c')

?