- #1

- 11

- 0

2D: polar coordinates - dA = r dr dtheta

3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr

4D: ?

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- Thread starter areslagae
- Start date

- #1

- 11

- 0

2D: polar coordinates - dA = r dr dtheta

3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr

4D: ?

- #2

- 316

- 0

x1 = r sin(theta1) sin(theta2) cos(phi)

x2 = r sin(theta1) sin(theta2) sin(phi)

x3 = r sin(theta1) cos(theta2)

x4 = r cos(theta1)

from which you can compute the hypervolume element.

- #3

- 11

- 0

Is "4-D spherical coordinates" established terminology?

Is this the "standard" transformation? I guess there are other ones?

- #4

- 316

- 0

Is "4-D spherical coordinates" established terminology?

Is this the "standard" transformation? I guess there are other ones?

I just checked wikipedia. There, the generalization to arbitrary dimension is called http://en.wikipedia.org/wiki/Hypersphere#Hyperspherical_coordinates". They are the same that I gave you in the 4-D case except for the order of the coordinates.

I don't know what the standard term in the case n=4 is.

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