The parametrization of the sphere:

appears in my book without explanation. Any help on how to derive it? (I played with it and found the coordinates correspond to latitude and longitude).

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- May 15th 2009, 04:14 PMmyrererparametrization
The parametrization of the sphere:

appears in my book without explanation. Any help on how to derive it? (I played with it and found the coordinates correspond to latitude and longitude). - May 16th 2009, 09:39 AMHallsofIvy
What do you know about "spherical coordinates"? In standard spherical coordinates, we have , the straight line distance from the origin to the point, , the angle a line from the origin to the point on the xy-plane directly below the given point makes with the x-axis (the same angle as in two-dimensional polar coordinates, and [itex]\phi[/itex] the line from the origin to the point makes with the xy-plane. You can think of the two angles as being "longitude" and "co-latitude" (since it is measured from the "north pole" rather than the "equator").

In spherical coordinates, , , and .

Here, I notice we have "sin" in z rather than "cos". Okay, they are using "latitude" rather than "co-latitude". That is, they are using so that

Finally, note the changes in notation: r instead of , instead of , and instead of . - May 16th 2009, 08:21 PMmyrerer