'Squaring' the Circle
Drag the GOLD dot to 'square' the circle geometrically -
when you do this two sets of parallel segments that are
perpendicular to one another are connected at the corners
by quarter circles.
Drag the slider to 'square' the circle algebraically -
when you do this a generalization of the circle relation
is plotted.
What conjectures do you have in each case about ratio of the area
of the 'squared circle' to that of the limiting square?