Barbier theorem

on curves of constant width

If the distance between any two parallel supporting straight lines to a curve is constant and equal to $a$, then the length of the curve is $\pi a$. Discovered by E. Barbier in 1860.

Comments

The original work of E. Barbier is [a1].

References

[a1]	E. Barbier, "Note sur le problème de l'ainguille et le jeu du joint couvert" J. Math. Pure Appl. , 5 (1860) pp. 273–286
[a2]	T. Bonnesen, W. Fenchel, "Theorie der konvexen Körper" , Springer (1934)