Polar curve
Enter an expression in θ, the associated polar curve will be plotted. Move a point along the curve, observe the speed vector, the Frenet-Serre frame of the tangent and its normal, and the osculating circle.
The radius of curvature is given by
R(θ)=(r'(θ)² + r(θ)²)^(3/2) / (2r'(θ)² + r(θ)² - r(θ) r''(θ))