Takayasu Kuwata

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Let us say that a plane figure F satisfies Steinhaus’ condition if for any positive integer n, there exists a figure Fn similar to F which satisfies the condition |Fn ∩ Z2| = n. For example, the circular disc satisfies Steinhaus’ condition. We prove that every compact convex region in the planeR2 satisfies Steinhaus’ condition. As for plane curves, it is(More)
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