Industrial Engineering & Management
Tamir, Ind Eng Manage 2014, 3:3
http://dx.doi.org/10.4172/2169-0316.1000e124
Editorial
Open Access
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
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
and 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.
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.
In the following the symbol of infinity is demonstrated by different
artworks. Figure 1 demonstrates the infinity symbol falling into a black
*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
Figure (1-12): Images related to the article .
Ind Eng Manage
ISSN: 2169-0316, IEM an open access journal
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.
Volume 3 • Issue 3 • 1000e124