AbstractArchimedes knew that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P,
the area of the region bounded by the parabola X and chord AB is four thirds of
the area of the triangle {\bigtriangleup ABP}. Recently,
the first two authors have proved that this fact is the characteristic property of parabolas.In this paper, we study strictly locally convex curves in the plane
{{\mathbb{R}}^{2}}.
As a result,
generalizing the above mentioned characterization theorem for parabolas,
we present two conditions, which are necessary and sufficient, for a strictly locally convex curve in the plane to be an open arc of a parabola.
Locally convex curves and the Bruhat stratification of the spin group
