Cardiod via osculating circles
Slider "n" determines the number of points uniformly distributed around a circle. Slider "m" cycles though those n points, drawing a circle centered at the selected point and passing through fixed point A. Toggle "show all circles" to display the circles centered at all the points all at once. With a little playing around, it should become evident what any other sliders/toggles do. Do a web search of the word "osculate" and ponder why it appears in the title of this activity.