(a) what effect would rotating the blue polygon have on the green graph?
(b) what effect would increasing the size of the blue polygon have on the green graph?
(c) can you describe the effect that the number of sides of the blue polygon has on the graph? as n gets larger, what shape does the blue polygon converge to? what graph does the green graph converge to?
(d) to which points on the green graph do the corners of the blue polygon correspond with? In what ways are those points on the graph different from other points on the graph?
(e) In the blue polygon, there are straight line segments connecting the corners. Is the same true in the green graph? (for octagons and higher, it looks like straight line segments between the corners... but are they truly straight? Can you explain why or why not).
(f) if the graph had been measuring the x-coordinate instead of the y-coordinate, how would it have been different? the same?
(g) for students that have had trigonometry: can you find an equation for these graph when the polygon is a triangle? a square? an n-gon?