Recent content by aplrt

Basically, it is a mapping from a disk to a 3-sphere (hypersphere) - a point (x2,x3,x4) in R3 is mapped to the 3-sphere by (sqrt(1-x2^2-x3^3-x4^),x2,x3,x4)=(x1,x2,x3,x4). I need the magnitude of the gradient to see how evenly or how far apart the points are mapped, but using the first expression...

Thank you for your reply! I'm still confused though, how will it look like, will it be \[\nabla Y = (\frac{-x_{2}}{\sqrt{1-...}}+1,\frac{-x_{3}}{\sqrt{1-...}}+1,\frac{-x_{4}}{\sqrt{1-...}}+1)\] or will it look like \[\nabla Y =...

I'm a bit confused here. If I have Y(x2,x3,x4)=(sqrt(1-x2^2-x3^2-x4^2),x2,x3,x4), how do I find the magnitude of the gradient? I know that for Y(s)=(sqrt(1-s^2),s) the gradient is (-s/sqrt(1-s^2),s) and the magnitude of the gradient is 1/sqrt(1-s^2), and I'm supposed to get an expression similar...