A140087 Decimal expansion of a lower bound of the area of a convex universal cover for a unit length curve.

2, 3, 2, 2, 3, 9, 2, 1, 0

Offset

0,1

Comments

Abstract: In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.

References

P. Brass, W. Moser, and J. Pach, Research Problems in Discrete geometry, Springer-Verlag, 2005.

Links

Table of n, a(n) for n=0..8.

Tirasan Khandhawit, Dimitrios Pagonakis, and Sira Sriswasdi, Lower Bound for Convex Hull Area and Universal Cover Problems, arXiv:1101.5638 [math.MG], 2011.

T. Khandhawit and S. Sriswasdi, An Improved Lower Bound for Moser's Worm Problem, arXiv:math/0701391 [math.MG], 2007-2009.

Example

0.232239...

Crossrefs

Sequence in context: A307835 A341651 A017828 * A174329 A295312 A212174

Adjacent sequences: A140084 A140085 A140086 * A140088 A140089 A140090

Keyword

cons,nonn

Author

Jonathan Vos Post, Jan 31 2011

Status

approved