Hypocycloids

Find a formula for the number of points on a hypocycloid in terms of the parameters a and b.

Plot the hypocycloid xy3(t) = [(a-b)cos(t)+b cos((a-b)t/b), (a-b)sin(t)-b sin((a-b)t/b)].
Vary the values of a and b. Count the number of points on each hypocycloid and look for a pattern.

For values of b greater than 6, you will need to increase the domain of t from 0t30 to 0t90 to complete the graphs.

If you make the values of b greater than the value of a, you will need to increase the range values of x and y and increase the domain values of t.
To help discover the formula, enter the values for a, b, and the number of points on the hypocycloid into the following table (Hint: keep "a" constant and vary the value of "b"):