Suppose a circle of radius r rolls at the rate of 1 radian per unit time along theinside of a circle of radius b > r. The curve traced out by a point on the circumference of the rolling circle is a hypocycloid. See figure below.

Suppose a circle of radius r rolls at the rate of 1 radian per unit time along theinside of a circle of radius b > r. The curve traced out by a point on the circumference of the rolling circle is a hypocycloid. See figure below.

(a) Find a path for the hypocycloid.

(b) What kind of curves do you get when b= 2r?

(c) Let b=nr for some positive integer n >2. What can you say about the numberof cusps on the graph? Remark: Try to plot a couple of these with Matlab.

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"