So the parametric equations of a hypersurface in VN are x^1=acos(u^1) x^2=asin(u^1)cos(u^2) x^3=asin(u^1)sin(u^2)cos(u^3) ... x^(N-1)=asin(u^1)sin(u^2)sin(u^3)...sin(u^(N-2))cos(u^(N-1)) x^N=asin(u^1)sin(u^2)sin(u^3)...sin(u^(N-2))sin(u^(N-1)) where a is a constant. How do I find the single equation of the hypersurface? And then from this how can it be determined whether the points (1/2a,0,0,...,0) and (0,0,0,...0,2a) are on the same or opposite sides of the surface? Any insight will be appreciated. Thanks. I ask another question when this thing is resolved in my mind.