1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    N/A

    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

    NascentOxygen

    User Avatar

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook