Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T06:22:49.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Partitioning Intervals, Spheres and Balls into Congruent Pieces

Published online by Cambridge University Press:  20 November 2018

Stanley Wagon
Stanley Wagon*
Affiliation:
Smith College Northampton Massachusetts 01063, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We survey results on partitioning some common sets into m congruent pieces, and prove that a ball in Rn cannot be so partitioned if 2 ≤ m ≤ n.

Keywords

51F2051M20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 337 - 340
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Cater, F. S., P 284,, Can. Math. Bull. 24 (1981) 382-383.Google Scholar
2. Dekker, T. J. and de Groot, J., Decompositions of a sphere, Proc. Int. Cong. Math. 2 (1954) 209.Google Scholar
3. Dekker, T. J. and de Groot, J., Decompositions of a sphere, Fund. Math. 43 (1956) 185-194.Google Scholar
4. Edelstein, M., On isometric complementary subsets of the unit hall, preprint.Google Scholar
5. Gustin, W., Partitioning an interval into finitely many congruent parts, Ann. Math. 54 (1951) 250-261.Google Scholar
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. Mycielski, J., On the paradox of the sphere, Fund. Math. 42 (1955) 348-355.Google Scholar
8. Mycielski, J., P166, Coll. Math. 4 (1957) 240.Google Scholar
9. Mycielski, J., On the decomposition of a segment into congruent sets and related problems, Coll. Math. 5 (1957) 24-27.Google Scholar
10. Robinson, R. M., On the decomposition of spheres, Fund. Math. 34 (1947) 246-260.Google Scholar
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. Sierpiński, W., On the congruence of sets and their equivalence by finite decomposition, Lucknow, 1954, Reprinted, Bronx: Chelsea, 1967.Google Scholar
13. Von Neumann, J., Die Zerlegung Eines Intevalle In Abzählbar Viele Kongruente Teilmengen, Fund. Math. 11 (1928) 230-238.Google Scholar