Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What's the analogue to spherical coordinates in $n$-dimensions? For example, for $n=2$ the analogue are polar coordinates $r,\theta$, which are related to the Cartesian coordinates $x_1,x_2$ by

$$x_1=r \cos \theta$$ $$x_2=r \sin \theta$$

For $n=3$, the analogue would be the ordinary spherical coordinates $r,\theta ,\varphi$, related to the Cartesian coordinates $x_1,x_2,x_3$ by

$$x_1=r \sin \theta \cos \varphi$$ $$x_2=r \sin \theta \sin \varphi$$ $$x_3=r \cos \theta$$

So these are my questions: Is there an analogue, or several, to spherical coordinates in $n$-dimensions for $n>3$? If there are such analogues, what are they and how are they related to the Cartesian coordinates? Thanks.

share|improve this question
2  
Hyperspherical coordinates are on Wikipedia. –  anon Aug 9 '11 at 19:22
add comment

1 Answer 1

up vote 5 down vote accepted

These are hyperspherical coordinates. You can see an example of them being put to use in this answer.

share|improve this answer
    
That's really funny, because I happen to read that answer just yesterday. And I was going to reference it for this question too. –  mixedmath Aug 9 '11 at 19:29
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.