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MathGroup Archive 2000

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Area of an Epicycloid ???

  • To: mathgroup at
  • Subject: [mg21393] Area of an Epicycloid ???
  • From: "Guybrush Threepwood" <guybrush_ at>
  • Date: Mon, 3 Jan 2000 03:12:25 -0500 (EST)
  • Organization: bingo e.V. (Buergernetz Ingolstadt e.V.)
  • Sender: owner-wri-mathgroup at

hello all !

im just trying to calculate the area between the epicyloid curve and the big
circle !
the problem is that there are some x coordinates which have 2 y values....
so i cant just simply integrate ! maybe someone of you has a hint for me !
Someone told me that maybe polar coordinates could be helpfull... what do ya
think ?

parameter form formula for epicycloids:

x(t) = (R+r) * cos (t) - r * cos ((R+r)*t / r )
y(t) = (R+r) * sin (t) -  r * sin ((R+r) *t /r )

thanks in advance & bye

Steve martins !

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