A point on just one tangent line is on the conic. The secant lines are the approximations to the tangent line. Let ABCDEF be a hexagon formed by six tangent lines of a conic section. It is always orthogonal to the unit tangent and normal vectors at . Therefore, is the tangent to the parabola at P. The equation of the tangent at point formula 125 has the form formula 126. Another way to think about tangent vectors is as directional derivatives. Liouville's theorem implies invariance of a kinematic measure on the unit tangent bundle. The slope of the tangent of both curves equals -formula 32. This is continuous with a tangent to the tip circle. This mapping can be performed by an inversion of the sphere onto its tangent plane. Note that the Savage and Tangent loss are not convex. The design warp is zero for both tangent and curved track. In 1821, Fresnel derived formulae equivalent to his sine and tangent laws Eqs. This old definition prevents inflection points from having any tangent.