At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...

At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...

At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...

In this note we prove that every network code over Fq may be realized taking some of the osculating spaces of a smooth projective curve.

At every point, a smooth plane curve can be approximated, to second order, by circle; this circle is called osculating. One may think of the osculating as passing through three infinitesimally close points curve. A vertex point at which hyper-osculates: it approximates third order. Equivalently, critical curvature function. Consider (necessarily non-closed) curve, free from vertices. The classi...

An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 — or, equivalently, the derivatives of fj and fk are both parallel to fi. The Frenet frame (t,p,b) along a space curve is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent ...

For a given real generic curve γ : S1 → Pn let Dγ denote the ruled hypersurface in Pn consisting of all osculating subspaces to γ of codimension 2. In this short note we show that for any two convex real projective curves γ1 : S1 → Pn and γ2 : S1 → Pn the pairs (Pn, Dγ1 ) and (Pn, Dγ2 ) are homeomorphic. §0. Preliminaries and results Definition. A smooth curve γ : S → P is called nondegenerate ...