Digital sundials, paradoxical sets, and vitushkin’s conjecture
ABSTRACT In recent years, life has become 'digitalized'. Familiar clock and watch faces are being replaced by digital readouts; digital displays are ousting the dials on weighing machines and voltmeters and the scales on thermometers. This article is concerned with the ultimate in digitalization-- we show how one of the most ancient of measuring devices, the sundial, may be replaced by a digital counterpart. An early reference is contained in Isaiah XXXVIII v8 where a sundial records a 10 ~ reversal of the earth's rotation as a prophetic sign. Many fine and varied examples of traditional sundials may be seen in the courts of medieval castles and houses or of ancient
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ABSTRACT: For arbitrary integers d,m with d>m⩾1, we construct a Cantor set in Rd such that its projection onto each m-dimensional plane has dimension (m−1). This example gives a partial answer to the question of J. Cobb (1994).Topology and Its Applications - TOPOL APPL. 01/2010; 157(4):745-751.
Article: Holographic sundial.[Show abstract] [Hide abstract]
ABSTRACT: A holographic sundial, to our knowledge the first sundial that does not use a gnomen or shadow-casting device, is designed and demonstrated. The accuracy of the device is measured and analyzed.Optics Letters 09/1990; 15(17):929-31. · 3.39 Impact Factor