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Equation of a Hypocycloid

  1. Nov 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Find parametric equations for the hypocycloid that is produced when we track a point on a circle of radius 1/4 that rotates inside a circle of radius 1. Show that these equations are equivalent to (sin^3 t, cos^3 t).

    2. Relevant equations


    3. The attempt at a solution

    I have the intended solution except for one step. The book claims that the small circle rotates 3 times every time it rotates once inside the big circle. That makes sense because of how the points line up... But the circumference of the big circle is 4 times that of the small one, and the surfaces are always touching, so why isn't it 4 times?
  2. jcsd
  3. Nov 4, 2011 #2


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    Staff: Mentor

    If it generates an astroid, then radii ratios are 1:4 http://en.wikipedia.org/wiki/Hypocycloid" [Broken]
    Last edited by a moderator: May 5, 2017
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