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4D angular coordinate system and corresponding hypervolume element

  1. Mar 4, 2009 #1
    I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element".

    2D: polar coordinates - dA = r dr dtheta
    3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr
    4D: ?
  2. jcsd
  3. Mar 4, 2009 #2
    4-D spherical coordinates:

    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.
  4. Mar 4, 2009 #3

    Is "4-D spherical coordinates" established terminology?
    Is this the "standard" transformation? I guess there are other ones?
  5. Mar 4, 2009 #4
    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.
    Last edited by a moderator: Apr 24, 2017
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