Barbier theorem

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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.


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


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