# Barbier theorem

From Encyclopedia of Mathematics

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) |

**How to Cite This Entry:**

Barbier theorem.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Barbier_theorem&oldid=39403

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article