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A140087 Decimal expansion of a lower bound of the area of a convex universal cover for a unit length curve. 0
2, 3, 2, 2, 3, 9, 2, 1, 0 (list; constant; graph; refs; listen; history; text; internal format)
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

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

LINKS

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

Tirasan Khandhawit, Dimitrios Pagonakis, Sira Sriswasdi, Lower Bound for Convex Hull Area and Universal Cover Problems , Jan 28, 2011.

Khandhawit, T. and Sriswasdi, S. An Improved Lower Bound for Moser's Worm Problem, v2., June 5, 2009.

EXAMPLE

0.232239...

CROSSREFS

Sequence in context: A053812 A177865 A017828 * A174329 A212174 A160558

Adjacent sequences:  A140084 A140085 A140086 * A140088 A140089 A140090

KEYWORD

cons,nonn

AUTHOR

Jonathan Vos Post, Jan 31 2011

STATUS

approved

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Last modified July 22 00:13 EDT 2017. Contains 289648 sequences.