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- W4302201601 abstract "Here is an example of a plane set of vanishing area and consisting of line-segments whose directions cover an angle : let E be a Cantor set of dissection ratio 1/4 (therefore dimension 1/2) carried by the horizontal axis and E' the image of E by an homothetic transformation of ratio 2 whose center is not on the horizontal axis ; the union of the line segments joining E and E' is the set in question. The example was given in 1969 by the author with a wrong proof. The present article contains a short proof based on the projection theorem of Besicovitch, and a long proof resulting from the investigation of the arithmetic, geometric and analytic properties of the horizontal sections of the set. This investigation copies the study by Richard Kenyon of a similar problem. Variations of the construction are provided in the plane and in multidimensional spaces." @default.
- W4302201601 created "2022-10-06" @default.
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- W4302201601 date "2012-06-20" @default.
- W4302201601 modified "2023-10-14" @default.
- W4302201601 title "Sur un ensemble de Besicovitch." @default.
- W4302201601 hasPublicationYear "2012" @default.
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