|
|
|
|||||||
| Év szerint | Hónap szerint | Ugrás a hónaphoz | |||||||
Zsolt Lángi: Arclength of curves with the increasing chords property |
|
|||
|
|
||||
|
||||
| We say that a curve $\gamma$ satisfies the increasing chords property, if for any points $a,b,c,d$ in this order on $\gamma$, the distance of $a,d$ is not smaller than the distance of $b,c$. Binmore asked the question in 1971 if there is a universal constant $C$ such that for any curve $\gamma$ in the Euclidean plane, satisfying the increasing chords property, if the endpoints of $\gamma$ are at unit distance apart, then the arclength of $\gamma$ is at most $C$. Larman and McMullen showed in 1972 that the constant $C=2\sqrt{3}$ satisfies this condition. Rote proved in 1991 that the optimal such constant is equal to $\frac{2\pi}{3}$. In this note we give an estimate for the arclengths of curves with the increasing chords property in Euclidean $d$-space, and generalize Rote's result for such curves in a normed plane with a strictly convex norm. Joint work with Adrian Dumitrescu and Sara Lengyel. |
||||
Esemény exportálása JEvents v3.1.8 Stable Copyright © 2006-2013
