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Some Possible and Some Impossible Tripartitions of the Plane
Published online by Cambridge University Press: 20 November 2018
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For each positive integer n it is possible to partition the Euclidean plane into n (disjoint) congruent connected sets [1], but if n > 2, it is impossible to partition the plane into n congruent continuumwise connected sets such that some one of the sets can be translated onto another one [2]. This paper is concerned with the possibility of partitioning the plane into three congruent sets without any topological restrictions whatever.
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- Copyright © Canadian Mathematical Society 1968