  Archimedes determined the center of gravity of a parabolic section as
follows. For a parabolic section between a parabola and any chord $AB$ on the
parabola, let us denote by $P$ the point on the parabola where the tangent is
parallel to $AB$ and by $V$ the point where the line through $P$ parallel to
the axis of the parabola meets the chord $AB$. Then the center $G$ of gravity
of the section lies on $PV$ called the axis of the parabolic section with
$PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane
curves satisfying the above center of gravity properties. As a result, we prove
that among strictly locally convex plane curves, those properties characterize
parabolas.

Differential Geometry