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Describing a Torus

  1. Oct 7, 2012 #1

    dpa

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    1. The problem statement, all variables and given/known data

    I need to derive the prarametric equation of a certain torus. defined by a unit circle on xz plane with center (a,0) and revolving about z-axis.

    2. Relevant equations

    * I dont know if this is relevent but here is something from wikipedia.
    Surfaces of revolution give another important class of surfaces that can be easily parametrized. If the graph z = f(x), a ≤ x ≤ b is rotated about the z-axis then the resulting surface has a parametrization r(u,∅)=(ucos∅,usin∅,f(u)).

    *

    3. The attempt at a solution

    I can derive the parametric equation of unit circle in xz plane which is given by:
    <sinu+a, cosu>

    I can also define the locus, (the path formed when constructing the torus, or let us say central circle of the torus), of the centre of the unit circle around Z axis in XY plane as above.
    if we consider ∅ be the angle of revolution of center of unit circle about z axis, we have
    <asin∅,acosb>.

    I have no idea how to connect these two elements.

    I would be infinitely obliged if someone could explain or provide a link for this.

    Thank You.
     
  2. jcsd
  3. Oct 7, 2012 #2

    LCKurtz

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  4. Oct 8, 2012 #3

    dpa

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    :smile:
    Thank You.
     
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