  Consider two elements in the tangent bundle of the Euclidean plane
$(x,X),(y,Y)\in T{\mathbb R}^2$. In this work we address the problem of
characterizing the paths of bounded curvature and minimal length starting at
$x$, finishing at $y$ and having tangents at these points $X$ and $Y$
respectively. This problem was first investigated in the late 50's by Lester
Dubins. In this note we present a constructive proof of Dubins' result giving
special emphasis on the geometric nature of this problem.
