Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-30T15:23:17.813Z Has data issue: false hasContentIssue false
  • English
  • Français

Sets Homothetic to their Intersection with a Translate

Published online by Cambridge University Press:  20 November 2018

J. B. Wilker
J. B. Wilker*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

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.

Inspired by a question of J. B. Miller, L. Fejes Tóth asked for a catalogue of those subsets of Euclidean n-space which are homothetic (similar and similarly situated) to their intersection with a suitably translated copy of themselves. For example, a triangle is homothetic to its intersection with an arbitrarily translated replica provided only that the intersection has non-void interior. In 3-space a cube is homothetic to its intersection with a replica translated part way along any body diagonal. With these two preliminary examples for motivation, let us make a definition.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 739 - 748
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Eggleston, H.G., A characterization of a simplex. Math. Ann. 193 (1971), 210-216. MR 44 #4637.Google Scholar
2. Grüber, P., Zur Charackterisierung konvexer Körper. Über einen Satz von Rogers und Shephard. I. Math. Ann. 181 (1969), 189-200. MR 39 #6171.Google Scholar
3. Grüber, P., Über eine Kennzeichnung der Simplices des Rn . Arch. Math. 22 (1971), 94-102. MR 44 #5859.Google Scholar
4. Rogers, C.A. and Shephard, G.C., The difference body of a convex body. Arch. Math. 8 (1957), 220-233. MR 19,1073.Google Scholar