Tangent lines, inflections, and vertices of closed curves
Tangent lines, inflections, and vertices of closed curves
We show that every smooth closed curve Γ immersed in Euclidean space R 3 satisfies the sharp inequality 2 ( P + I ) + V ≥ 6 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of …