So the parametric equations of a hypersurface in VN(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Two quick questions on subspaces (intro to tensor calc)

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