Geodesic
Partitioning Intervals, Spheres and Balls into Congruent Pieces
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 337-340

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

We survey results on partitioning some common sets into m congruent pieces, and prove that a ball in R n cannot be so partitioned if 2 ≤ m ≤ n.
DOI : 10.4153/CMB-1983-056-8
Mots-clés : 51F20, 51M20 
Wagon, Stanley. Partitioning Intervals, Spheres and Balls into Congruent Pieces. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 337-340. doi: 10.4153/CMB-1983-056-8
@article{10_4153_CMB_1983_056_8,
     author = {Wagon, Stanley},
     title = {Partitioning {Intervals,} {Spheres} and {Balls} into {Congruent} {Pieces}},
     journal = {Canadian mathematical bulletin},
     pages = {337--340},
     year = {1983},
     volume = {26},
     number = {3},
     doi = {10.4153/CMB-1983-056-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-056-8/}
}
TY  - JOUR
AU  - Wagon, Stanley
TI  - Partitioning Intervals, Spheres and Balls into Congruent Pieces
JO  - Canadian mathematical bulletin
PY  - 1983
SP  - 337
EP  - 340
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-056-8/
DO  - 10.4153/CMB-1983-056-8
ID  - 10_4153_CMB_1983_056_8
ER  - 
%0 Journal Article
%A Wagon, Stanley
%T Partitioning Intervals, Spheres and Balls into Congruent Pieces
%J Canadian mathematical bulletin
%D 1983
%P 337-340
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-056-8/
%R 10.4153/CMB-1983-056-8
%F 10_4153_CMB_1983_056_8

[1] 1. Cater, F. S., P 284,, Can. Math. Bull. 24 (1981) 382-383. Google Scholar

[2] 2. Dekker, T. J. and de Groot, J., Decompositions of a sphere, Proc. Int. Cong. Math. 2 (1954) 209. Google Scholar

[3] 3. Dekker, T. J. and de Groot, J., Decompositions of a sphere, Fund. Math. 43 (1956) 185-194. Google Scholar

[4] 4. Edelstein, M., On isometric complementary subsets of the unit hall, preprint. Google Scholar

[5] 5. Gustin, W., Partitioning an interval into finitely many congruent parts, Ann. Math. 54 (1951) 250-261. Google Scholar

[6] 6. Mazurkiewicz, S., Sur la décomposition d'un segment en une infinité d1ensembles non mesurables superposables deux à deux, Fund. Math. 2 (1921) 8-14. Google Scholar

[7] 7. Mycielski, J., On the paradox of the sphere, Fund. Math. 42 (1955) 348-355. Google Scholar

[8] 8. Mycielski, J., P166, Coll. Math. 4 (1957) 240. Google Scholar

[9] 9. Mycielski, J., On the decomposition of a segment into congruent sets and related problems, Coll. Math. 5 (1957) 24-27. Google Scholar

[10] 10. Robinson, R. M., On the decomposition of spheres, Fund. Math. 34 (1947) 246-260. Google Scholar

[11] 11. Ruziewicz, S., Une application de l'equation functionelle f(x + y) = f(x) + f(y) à la décomposition de la droite en ensembles superposables non mesurables, Fund. Math. 5 (1924) 92-95. Google Scholar

[12] 12. Sierpiński, W., On the congruence of sets and their equivalence by finite decomposition, Lucknow, 1954, Reprinted, Bronx: Chelsea, 1967. Google Scholar

[13] 13. Von Neumann, J., Die Zerlegung Eines Intevalle In Abzählbar Viele Kongruente Teilmengen, Fund. Math. 11 (1928) 230-238. Google Scholar

Cité par Sources :