Digital sundials, paradoxical sets, and Vitushkin's conjecture
type: Item
instance of: scholarly article
title: Digital sundials, paradoxical sets, and Vitushkin's conjecture
zbMATH Open document ID: 0609.28005
DOI: 10.1007/BF03023569
published in: The Mathematical Intelligencer
publication date: 1987-01-01T00:00:00Z
review text: A digital sundial is an ''object'' whose shadow at any given time shows the digits of that time. The existence of such a magic clock is a consequence of a more general result of the author on finding sets with prescribed projections [Proc. Lond. Math. Soc., III. Ser. 53, 48-64 (1986; Zbl 0602.28005)]. In this article the author discusses the underlying construction, earlier related results of Besicovitch, Davies and Marstrand, and a recent use of such constructions by the reviewer to disprove a conjecture in complex function theory.
reviewed by: Pertti Mattila
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 3985552
zbMATH Keywords: orthogonal projection
zbMATH Keywords: Hausdorff measure and dimension
zbMATH Keywords: Vitushkin's conjecture
zbMATH Keywords: digital sundial
zbMATH Keywords: sets with prescribed projections
Wikidata QID: Q123290642
author: Kenneth J. Falconer
MaRDI profile type: Publication
cites work: Q5809296
cites work: Q3714302
cites work: Sets with Prescribed Projections and Nikodym Sets
cites work: Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions
cites work: Smooth maps, null-sets for integralgeometric measure and analytic capacity
full work available at URL: https://doi.org/10.1007/bf03023569
OpenAlex ID: W1993059250
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description: scientific article; zbMATH DE number 3985552