Sets Homothetic to their Intersection with a Translate
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 739-748
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Wilker, J. B. Sets Homothetic to their Intersection with a Translate. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 739-748. doi: 10.4153/CMB-1975-128-5
@article{10_4153_CMB_1975_128_5,
author = {Wilker, J. B.},
title = {Sets {Homothetic} to their {Intersection} with a {Translate}},
journal = {Canadian mathematical bulletin},
pages = {739--748},
year = {1975},
volume = {18},
number = {5},
doi = {10.4153/CMB-1975-128-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-128-5/}
}
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