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My brother, who is in hospital atm and cannot verify by himself asked me to post the following question, thank you in advance, and sorry if the topic has already been covered, i do not have the math knowledge to look for it in the forums.

He wants to map, on the unit sphere with polar coordinates, the square with vertices $(0,1)$, $(1,0)$. $(-1,0)$, $(0,-1)$ with centre $(0,0)$ having $(0,1)$ and $(0,-1)$ as poles.

He wants to know if the map $(a,b)\mapsto (a\pi , \arcsin(b))$ is adequate or at least it works.

He would also like to know if there's a more clever way to do that.

Thank you.

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    This would map the point $(0,1)$ to the point $\left(0,\frac{\pi}{2}\right)$, which is not on the unit circle.2012-10-08
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    I don't see why people are voting to close. All of this personal information may be irrelevant, but the question is perfectly valid.2013-03-12

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