Inextensible domains
@article{Kallus2013InextensibleD, title={Inextensible domains}, author={Yoav Kallus}, journal={Geometriae Dedicata}, year={2013}, volume={173}, pages={177-184} }
We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that origin-symmetric inextensible domains are exactly the origin-symmetric convex domains with a circle of outer billiard triangles. We address a conjecture by Genin and Tabachnikov about convex domains, not necessarily symmetric, with a circle of outer billiard…
4 Citations
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It is found that the ball is a local pessimum in 3 dimensions, but not so in 4 and 5 dimensions.
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Given the n vertices of a convex polygon in cyclic order, can the triangle of maximum area inscribed in P be determined by an algorithm with O(n) time complexity? A purported linear-time algorithm by…
When is the Ball a Local Pessimum for Covering?
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We consider the problem of identifying the worst point-symmetric shape for covering n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…
References
SHOWING 1-10 OF 11 REFERENCES
On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards
- Mathematics
- 2006
Following a recent paper by Baryshnikov and Zharnitsky, we consider outer billiards in the plane possessing invariant curves consisting of periodic orbits. We prove the existence and abundance of…
Convex and Discrete Geometry
- Mathematics
- 2009
Geir Agnarsson, Jill Bigley Dunham.* George Mason University, Fairfax, VA. Extremal coin graphs in the Euclidean plane. A coin graph is a simple geometric intersection graph where the vertices are…
On a general method for maximizing and minimizing among certain geometric problems
- Mathematics20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979
Algorithms solving a number of problems concerned with finding inscribing or circumscribing polygons that maximize some measurement in linear time use the common approach of finding an initial solution with respect to a fixed bounding point and iteratively transforming this solution into a new solution withrespect to a new point.
Über eine Extremumeigenschaft der Ellipsen
- Mathematics
- 1939
© Foundation Compositio Mathematica, 1939, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…
Über die dichteste gitterf örmige lagerung kongruenter bereiche in der ebene und eine besondere art konvexer kurven
- Mathematics
- 1934
On irreducible convex domains, On the area and the densest packing of convex domains, On the minimum determinant and the circumscribed hexagons of a convex domain
- On lattice points in n-dimensional star bodies I-IV, Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen
- 1946
Compositio Math
- Compositio Math
- 1939
On lattice points in n-dimensional star bodies I–IV
- Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen
- 1946