Enter an expression in θ, the associated polar curve will be plotted. Move a point along the curve, observe the speed vector, the [url=https://en.wikipedia.org/wiki/Frenet%E2%80%93Serret_formulas]Frenet-Serre frame[/url] of the tangent and its normal, and the osculating circle.

The radius of curvature is given by[br]R(θ)=(r'(θ)² + r(θ)²)^(3/2) / (2r'(θ)² + r(θ)² - r(θ) r''(θ))