This demo shows the tangent plane for the displayed polar surface. Note that the intersection set of the tangent plane with the function graph allows us to classify the points of the surface into two categories: for some points in the domain, the tangent plane meets a neighborhood of the point (r₀,θ₀,f(r₀,θ₀) on the graph in a single point, whereas for other points, the tangent plane meets the graph in a pair of curves, or occasionally in a more complicated set of points.