This is a kind of silly-sounding question I never realized puzzled me until moments ago, when I looked up the algorithm for spherical coordinates in n dimensions.(adsbygoogle = window.adsbygoogle || []).push({});

In two dimensions, we have polar coordinates, consisting of r from 0 to ∞, and θ from 0 to 2π. In spherical coordinates, we have a third angle, from 0 to π, measured from the z-axis. Intuitively the reason for this is clear. So I wondered about n dimensions - is it the case that a 4-sphere requires an angle running only from 0 to π/2? Apparently not - all angles invoked for more than two dimensions run fron 0 to π. What in a mathematical sense, is special about the two-dimensional case that does not hold for higher dimensions?

I'm a final-year physics undergrad; I've taken courses in multilinear algebra, multivariable calculus, and complex caluculus, and I have a casual interest in topology and advanced geometry, but basically I do not have a good grasp of anything beyond the level of, say, Spivak's "Calculus on Manifolds".

EDIT: I realize this is somehow related to there being no straightforward 1d equivalent because you cannot account for parity in a continuous manner unlike higher dimensions, but that's as far as I get.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I N-spherical coordinate angle intervals

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for spherical coordinate angle |
---|

B Spherical Geometry (Two dimension ) Defining a metric |

I Can a tetrahedron have all dihedral angles rational? |

**Physics Forums | Science Articles, Homework Help, Discussion**