Difference between revisions of "Barbier theorem"
From Encyclopedia of Mathematics
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| − | ''on curves of constant width'' | + | {{TEX|done}} |
| + | ''on [[Constant width, curve of|curves of constant width]]'' | ||
| − | 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. |
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Barbier, "Note sur le problème de l'ainguille et le jeu du joint couvert" ''J. Math. Pure Appl.'' , '''5''' (1860) pp. 273–286</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> T. Bonnesen, W. Fenchel, "Theorie der konvexen Körper" , Springer (1934)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Barbier, "Note sur le problème de l'ainguille et le jeu du joint couvert" ''J. Math. Pure Appl.'' , '''5''' (1860) pp. 273–286</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> T. Bonnesen, W. Fenchel, "Theorie der konvexen Körper" , Springer (1934)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 17:28, 10 October 2016
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=17513
Barbier theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Barbier_theorem&oldid=17513
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article