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Some Possible and Some Impossible Tripartitions of the Plane

Published online by Cambridge University Press:  20 November 2018

Leroy F. Meyers
Leroy F. Meyers*
Affiliation:
The Ohio State University
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 415 - 421
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Problem E1515, The Amer. Math. Monthly, 69(1962) 312. Solution, ibid. 70 (1963) 95–96.Google Scholar
2. Meyers, Leroy F., Partition of the plane into finitely many isometric continuumwise connected sets. Bull. Acad. Polon. Sci., sér. sci. math., astr. etphys., 13 (1965) 533-535.Google Scholar