Difference between revisions of "Barbier theorem"
From Encyclopedia of Mathematics
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| − | If the distance between any two parallel supporting straight lines to a curve is constant and equal to | + | 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. |
Revision as of 01:15, 29 April 2014
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) |
How to Cite This Entry:
Barbier theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Barbier_theorem&oldid=31965
Barbier theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Barbier_theorem&oldid=31965
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article