Cardiod via perpendiculars to tangent lines
Study what's going on in this construction:
- Point A is the center of a circle of fixed radius.
- Point B is a point revolving along the circle
- A line is drawn perpendicular to the circle at point B.
- A perpendicular segment is drawn from fixed point C on the circle to the tangent line, meeting the tangent line at point D.
Slider "n" determines the number of points evenly distributed around a circle. Slider "m" cycles through those points, drawing a cord originating from the nth point, labeled "A." As point A increments one position at a time, slider "coeff" determines the number of positions that endpoint "B" jumps. With a little playing around, it should become evident what any other sliders/toggles do.