Thread: Hypocycloid Problem

"A hypocycloid is a curve traced by a fixed point P on a circle C with radius b as C rolls on the inside of a circle with the center on the origin and radius a. If the initial point P is (a,0) and the parameter is theta, then the parametric equation is

x = (a-b)cos(theta) + bcos((theta)(a-b)/b))
y = (a-b)sin(theta) + bsin((theta)(a-b)/b))

Question 1: Show that the parametric equation is correct"


This is the picture I drew out to clarify..



But I don't even know how to start explaining why it is correct... any suggestions?

Originally Posted by coolguy99

"A hypocycloid is a curve traced by a fixed point P on a circle C with radius b as C rolls on the inside of a circle with the center on the origin and radius a. If the initial point P is (a,0) and the parameter is theta, then the parametric equation is

x = (a-b)cos(theta) + bcos((theta)(a-b)/b))
y = (a-b)sin(theta) + bsin((theta)(a-b)/b))

Question 1: Show that the parametric equation is correct"

...

1. In my opinion the given equation describes an epicycloid. If you want to get a hypocycloid the equation should read:


2. The distance in your sketch which is labeled a - b is actually

3. To start:
- Determine where you can find in your sketch.
- Determine where you can find in your sketch.
- Calculate the corresponding distances which form the coordinates of the points placed on the cycloid.