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ISSN: 2169-0316
Industrial Engineering & Management
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Artistic Demonstrations by Euclidean Geometry: Possible in 2D but Impossible in 3D

Abraham Tamir*

Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel

*Corresponding Author:
Abraham Tamir
Department of Chemical Engineering
Ben-Gurion University of the Negev, Beer-Sheva, Israel
E-mail: [email protected]

Received May 12, 2014; Accepted May 13, 2014; Published May 21, 2014

Citation: Tamir A (2014) The Symbol of Infinity Represented by the Art. Ind Eng Manage 3:e124. doi: 10.4172/2169-0316.1000e124

Copyright: © 2014 Tamir A. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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infinity is a concept that has different meanings in mathematics, philosophy, cosmology and everyday language. However the common to all meanings is that infinity is something that its content is higher than everything else or a process that will never reach its end. The mathematical symbol of infinity is demonstrated in the different artworks that are the major subject of this article. The most accepted definition of infinity is “a quantity greater than any assignable quantity of the same kind”. Other definitions are as follows. In geometry it is related to the axioms where each straight line contains infinite number of points. In cosmology the major question is if the universe will expand a process that will continue until infinity. In physics the problem arises from the equations demonstrating physical reality the result of which is infinity. In fractals, one of the most unusual aspects of them is that their repeating and changing patterns are infinite. They can be magnified indefinitely without losing their structure; they have infinite perimeters. And finally infinity appears also in the Bible, in Job Chapter 5 verse 9:” Which does great things unreachable; marvellous things without number” where “without number” means infinity.

The word infinity comes from the Latin word infinitas or unboundeless. It was John Wallis, an English mathematician, who is credited with introducing the infinity symbol in 1655. He derived it from a Roman numeral for 1000 that was in turn derived from the Etruscan numeral for 1000, which looked somewhat like Imageand was sometimes used to mean “many.” Another conjecture is that he derived it from the Greek letter omega ω, the last letter in the Greek alphabet. The infinity symbol is also sometimes depicted as a special variation of the ancient snake symbol. The snake is twisted into the horizontal eight configurations while engaged in eating its own tail, a uniquely suitable symbol for endlessness.

the following the symbol of infinity is demonstrated by different artworks. Figure 1 demonstrates the infinity symbol falling into a black hole. The right hand side of Figure 2 entitled “The False Mirror” is the artwork of the Belgian surrealist artist Rene Magritte. A giant eye is formed as a frame of a blue sky with clouds. The pupil of the eye creates a dead centre in a sharp colour contrast to the white and blue of the sky, and also with a contrast of form–the hard outline of the pupil against the soft curves and natural form of the clouds. Surprisingly, the combination of the original artwork on the right with its mirror image creates the symbol of infinity. Figures 3-5 are additional demonstration of infinity where in Figure 6 it is based on the moustache of Salvador Dali, a Spanish surrealist painter, whose image is demonstrated. On his moustache Dali said the following: “Since I don’t smoke, I decided to grow a moustache – it is better for the health.” Figure 7 was painted by the Flemish Renaissance painter Pieter Bruegel the Elder where Figures 8-12 by the Dutch graphic artist M.C.Escher. Figure 8 demonstrates infinity in two ways. The first by the symbol and the second by the circles the diameters of which is continuously decreasing. Figure 9 entitled “Swans” and Figure 10 demonstrate infinity on the basis of the moebius strip, which is a surface that has only one boundary. Figures 11 and 12 entitled “Circle Limit III” and “Circle Limit IV” are composed of an astounding combination of an identical single fish in Figure 11 and a combination of two animals in Figure 12. In addition the components are diminishing in size towards the circumference of the circle. In addition the two patterns demonstrate fractals, namely geometric patterns that are repeated at ever-smaller scales. Moreover, with respect to the number of shapes, the two paintings may be considered as demonstrating the tending to infinity of the number of shapes.

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