Time: October 21, 2025 12:30 pm

Location: Riesz lecture hall, Bolyai Building, Aradi vértanúk tere 1., Szeged, Hungary

Abstract: 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.

The seminar's Zoom link. The paasword is the first six digits after the decimal point of the packing density of the circle.