Lattice points on similar figures and conics
T Kuwata, H Maehara - Graphs and Combinatorics, 2011 - Springer
T Kuwata, H Maehara
Graphs and Combinatorics, 2011•SpringerLet us say that a plane figure F satisfies Steinhaus' condition if for any positive integer n,
there exists a figure F n similar to F which satisfies the condition| F_n ∩\mathbb Z^ 2|= n. For
example, the circular disc satisfies Steinhaus' condition. We prove that every compact
convex region in the plane\mathbb R^ 2 satisfies Steinhaus' condition. As for plane curves, it
is known that the circle satisfies Steinhaus' condition. We consider Steinhaus' condition for
other conics, and present several results.
there exists a figure F n similar to F which satisfies the condition| F_n ∩\mathbb Z^ 2|= n. For
example, the circular disc satisfies Steinhaus' condition. We prove that every compact
convex region in the plane\mathbb R^ 2 satisfies Steinhaus' condition. As for plane curves, it
is known that the circle satisfies Steinhaus' condition. We consider Steinhaus' condition for
other conics, and present several results.
Abstract
Let us say that a plane figure F satisfies Steinhaus’ condition if for any positive integer n, there exists a figure F n similar to F which satisfies the condition . For example, the circular disc satisfies Steinhaus’ condition. We prove that every compact convex region in the plane satisfies Steinhaus’ condition. As for plane curves, it is known that the circle satisfies Steinhaus’ condition. We consider Steinhaus’ condition for other conics, and present several results.
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