The function f is geometrically interpreted as a curve in the plane in two ways: first as its graph y=f(x) in rectangular (Cartesian) coordinates as the locus of points (x, f(x)), and second as its graph r=f(θ) in polar coordinates as the locus of (rectangular) points (r cos(θ), r sin(θ)). A bubble traces out corresponding points on these two graphs between θ_min and θ_max, shading in the area "under" the polar graph, green for positive area and red for negative area.