\[\kappa ~=~ \frac{\dfrac{d^2y}{\dx^2}}{\left(1 + \left(\Dydx\right)^2\right)^{3/2}} ~=~ \frac{\dfrac{x'(t)\,y''(t) ~-~ y'(t)\,x''(t)}{(x'(t))^3}}{\left(1 \;+\; \left(\dfrac{y'(t)}{x'(t)}\right)^2\rig...κ=d2y\dx2(1+(\Dydx)2)3/2=x′(t)y″(t)−y′(t)x″(t)(x′(t))3(1+(y′(t)x′(t))2)3/2=x′(t)y″(t)−y′(t)x″(t)((x′(t))2)3/2(1+(y′(t)x′(t))2)3/2Simplifica el denominador para obtener la fórmula de curvatura paramétrica:
