  The Horizontal Chord Theorem states that if a continuous curve connects
points $A$ and $B$ in the plane, then for any integer $k$ there are points $C$
and $D$ on the curve such that $\overrightarrow{AB}=k \overrightarrow{CD}$. In
this note, we discuss a few combinatorial-analysis problems related to this
theorem and introduce a different formulation that gives way to generalizations
on graphs.
