Geodesic
Some Possible and Some Impossible Tripartitions of the Plane
Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 415-421

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Meyers, Leroy F. Some Possible and Some Impossible Tripartitions of the Plane. Canadian mathematical bulletin, Tome 11 (1968) no. 3, pp. 415-421. doi: 10.4153/CMB-1968-048-4
@article{10_4153_CMB_1968_048_4,
     author = {Meyers, Leroy F.},
     title = {Some {Possible} and {Some} {Impossible} {Tripartitions} of the {Plane}},
     journal = {Canadian mathematical bulletin},
     pages = {415--421},
     year = {1968},
     volume = {11},
     number = {3},
     doi = {10.4153/CMB-1968-048-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-048-4/}
}
TY  - JOUR
AU  - Meyers, Leroy F.
TI  - Some Possible and Some Impossible Tripartitions of the Plane
JO  - Canadian mathematical bulletin
PY  - 1968
SP  - 415
EP  - 421
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-048-4/
DO  - 10.4153/CMB-1968-048-4
ID  - 10_4153_CMB_1968_048_4
ER  - 
%0 Journal Article
%A Meyers, Leroy F.
%T Some Possible and Some Impossible Tripartitions of the Plane
%J Canadian mathematical bulletin
%D 1968
%P 415-421
%V 11
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-048-4/
%R 10.4153/CMB-1968-048-4
%F 10_4153_CMB_1968_048_4

[1] 1. Problem E1515, The Amer. Math. Monthly, 69(1962) 312. Solution, ibid. 70 (1963) 95–96. Google Scholar

[2] 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

Cité par Sources :