First, students will learn two ways of deriving the equations of a cycloid.
Next, students will learn how to derive the equations of an epicycloid.
Deriving the Equations of an Epicycloid by Xander Gouws
After that, students will learn how to derive the equations of a hypocycloid.
Conclude by giving your students these challenges:
Draw four circles, such that each circle contains an odd number of roses, each circle contains a different number of roses, and no two circles touch or intersect:
Here's the solution:
Source: Test Your Math IQ by Steve Ryan