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| The Golden Number is not mathematical imagination, but a natural principle related to the laws of equilibrium |
[Allah has appointed a measure for all
things.]
(Qur’an,
65: 3)
The
Wikipedia encyclopaedia describes beauty as ‘the
phenomenon of the experience of pleasure, through the perception of
balance’. Everyone admires beauty in nature and the unique balance found
in it. Some say that this balance and perception of beauty is due to the
Golden number or the ratio that gives certain things their exquisitness.
If
a pleasing or exceedingly balanced form is achieved in terms of elements of
application or function, it is there that we may look for a function of the
Golden Number. The Golden Number is a product not of mathematical
imagination, but of a natural principle related to the laws of equilibrium.[1]
What
do the pyramids in Egypt, Leonardo da Vinci’s portrait of the Mona Lisa, sunflowers, the snail,
the pine cone and your fingers all have in common?
The
answer to this question lies hidden in a sequence of numbers discovered by
the Italian mathematician Fibonacci. The characteristic of these numbers,
known as the Fibonacci numbers, is that each one consists of the sum of the
two numbers before it.[2]
Fibonacci
numbers
0,
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,
…
Fibonacci
numbers have an interesting property. When you divide one number in the
sequence by the number before it, you obtain numbers very close to one
another. In fact, this number is fixed after the 13th number in
the series. This number is known as the “golden ratio.”
GOLDEN
RATIO = 1.618
233
/ 144 = 1.618
377
/ 233 = 1.618
610
/ 377 = 1.618
987
/ 610 = 1.618
1597
/ 987 = 1.618
2584
/ 1597 = 1.618
The
Golden Ratio
When
conducting their researches or setting out their products, artists,
scientists and designers take the human body, the proportions of which are
set out according to the golden ratio, as their measure. Leonardo da Vinci
and Le Corbusier took the human body, proportioned according to the golden
ratio, as their measure when producing their designs. The human body,
proportioned according to the golden ratio, is taken as the basis also in
the Neufert, one of the most important reference books of modern-day
architects.
The
Golden Ratio in the Human Body
The
“ideal” proportional relations that are suggested as existing among
various parts of the
average human body and that approximately meet the golden ratio values can
be set out in a general plan as follows:[3]
The
M/m level (shown in the table to the right) is always equivalent to the
golden ratio. M/m = 1.618
The
first example of the golden ratio in the average human body is that when the
distance between the navel and the foot is taken as 1 unit, the height of a
human being is equivalent to 1.618. Some other golden proportions in the
average human body are:
-
The
distance between the finger tip and the elbow / distance between the
wrist and the elbow
-
The
distance between the shoulder line and the top of the head / head length
-
The
distance between the navel and the top of the head / the distance
between the shoulder line and the top of the head
-
The
distance between the navel and knee / distance between the knee and the
end of the foot
The
Human Hand
Lift
your hand from the computer mouse and look at the shape of your index
finger. You will in all likelihood witness a golden proportion there.
Our
fingers have three sections. The proportion of the first two to the full
length of the finger gives the golden ratio (with the exception of the
thumbs). You can also see that the proportion of the middle finger to the
little finger is also a golden ratio.[4]
You
have two hands, and the fingers on them consist of three sections. There are
five fingers on each hand, and only eight of these are articulated according
to the golden number: 2, 3, 5, and 8 fit the Fibonacci numbers.
The
Golden Ratio in the Human Face
There
are several golden ratios in the human face. Do not pick up a ruler and try
to measure people’s faces, however, because this refers to the “ideal
human face” determined by scientists and artists.
For
example, the total width of the two front teeth in the upper jaw over their
height gives a golden ratio. The width of the first tooth from the centre to
the second tooth also yields a golden ratio. These are the ideal proportions
that a dentist may consider. Some other golden ratios in the human face are:
-
Length of
face / width of face
-
Distance
between the lips and where the eyebrows meet / length of nose
-
Length of
face / distance between tip of jaw and where the eyebrows meet
-
Length of
mouth / width of nose
-
Width of
nose / distance between nostrils
-
Distance
between pupils / distance between eyebrows
Golden
Proportion in the Lungs
In
a study carried out between 1985 and 1987,[5]
the American physicist B. J. West and Dr. A. L. Goldberger revealed the
existence of the golden ratio in the structure of the lung. One feature of
the network of the bronchi that
constitutes the lung is that it is asymmetric. For example, the windpipe
divides into two main bronchi, one long (the left) and the other short (the
right). This asymmetrical division continues into the subsequent
subdivisions of the bronchi.[6]
It was determined that in all these divisions the proportion of the short
bronchus to the long was always 1/1.618.
The
Golden Rectangle and the Design in the Spiral
 |
| A rectangle, the proportion of whose sides is equal to the golden ratio is known as a “golden rectangle” |
A
rectangle, the proportion of whose sides is equal to the golden ratio is
known as a “golden rectangle.” A rectangle whose sides are 1.618 and 1
unit long is a golden rectangle. Let us assume a square drawn along the
length of the short side of this rectangle and draw a quarter circle between
two corners of the square. Then, let us draw a square and a quarter circle
on the remaining side and do this for all the remaining rectangles in the
main rectangle. When you do this you will end up with a spiral.
The
British aesthetician William Charlton explains the way that people find the
spiral pleasing and have been using it for thousands of years stating that
we find spirals pleasing because we are easily able to visually follow them.[7]
The
spirals based on the golden ratio contain the most incomparable designs you
can find in nature. Examples we can give of this are the spiral sequences on
the sunflower and the pine cone.
The
Design in Sea Shells
When
investigating the shells of mollusks, which live at the bottom of the sea,
the form and the structure of the internal and external surfaces of the
shells attracted scientists’ attention.
The
internal surface is smooth, while the outside surface is fluted. The
mollusk’s body is inside the shell. The outside edges of the shell augment
its rigidity and, thus, increase its strength. The shell’s form is
astonishing in its perfection highlighting the beauty of its creation. The
spiral idea in shells is expressed in the perfect geometrical form, in a
surprisingly beautiful, “sharpened” design.[8]
The
shells of most mollusks grow in a logarithmic spiral manner. There can be no
doubt, of course, that these animals are unaware of even the simplest
mathematical calculation, let alone logarithmic spirals. So how is it that
the creatures in question can know that this is the best way for them to
grow? How do these animals, that some scientists describe as
“primitive,” know that this is the ideal form for them? It is impossible
for growth of this kind to take place in the absence of a consciousness or
intellect. That consciousness exists neither in mollusks nor, despite what
some scientists would claim, in nature itself. It is totally irrational to
seek to account for such a thing in terms of chance. This design can only be
the product of the Almighty Allah.
 |
| An example of perfect geometry |
Growth
of this kind was described as “gnomic growth” by the biologist Sir
D’Arcy Thompson, an expert on the subject, who stated that it was
impossible to imagine a simpler system, during the growth of a seashell,
than which was based on widening and extension in line with identical and
unchanging proportions. As he pointed out, the shell constantly grows, but
its shape remains the same.[9]
One
can see one of the best examples of this type of growth in a nautilus, just
a few centimetres in diameter. C. Morrison describes this growth process,
which is exceptionally difficult to plan even with human intelligence,
stating that along the nautilus shell, an internal spiral extends consisting
of a number of chambers with mother-of-pearl (calcium carbonate and
conchiolin secreted by the mantle of mollusks) lined walls. As the animal
grows, it builds another chamber at the mouth of the spiral shell
larger than the one before it, and moves forward into this larger
area by closing the door behind it with a layer of mother-of-pearl.[10]
Growth
in a spiral form in the animal world is not restricted to the shells of
mollusks. Animals such as antelopes, goats and rams complete their horn
development in spiral forms based on the golden ratio.[11]
The
Golden Ratio in the Hearing and Balance Organ
The
cochlea in the human inner ear serves to transmit sound vibrations. This
bony structure, filled with fluid, has a logarithmic spiral shape with a
fixed angle of α=73°43´ containing the golden ratio.
The
Golden Ratio in DNA
The
molecule in which all the physical features of living things are stored,
too, has been created in a form based on the golden ratio. The DNA molecule,
the very program of life, is based on the golden ratio. DNA consists of two
intertwined perpendicular helixes. The length of the curve in each of these
helixes is 34 angstroms and the width 21
angstroms. (1 angstrom is one hundred millionth of a centimetre.) 21 and 34
are two consecutive Fibonacci numbers.
The
Golden Ratio in Snow Crystals
The
golden ratio also manifests itself in crystal structures. Most of these are
in structures too
minute to be seen with the naked eye. Yet you can see the golden ratio in
snow flakes. The various long and short variations and protrusions that
comprise the snow flake all yield the golden ratio.[12]
The
Golden Ratio in Space
In
the universe there are many spiral galaxies containing the golden ratio in
their structures.
The
Golden Ratio in Physics
You
encounter Fibonacci series and the golden ratio in fields that fall under
the sphere of physics. When a light is held over two contiguous layers of
glass, one part of that light passes through, one part is absorbed, and the
rest is reflected. What happens is a “multiple reflection.” The number
of paths taken by the ray inside the glass before it emerges again depends
on the number of reflections it is subjected to. In conclusion, when we
determine the number of rays that re-emerge, we find that they are
compatible with the Fibonacci numbers.[13]
The
fact that a great many unconnected animate or inanimate structures in nature
are shaped according to a specific mathematical formula is one of the
clearest proofs that these have been specially designed. The golden ratio is
an aesthetic rule well known and applied by artists. Works of art based on
that ratio represent aesthetic perfection. Plants, galaxies,
micro-organisms, crystals and living things designed according to this rule
imitated by artists are all examples of Allah’s superior artistry. Allah
reveals in the Qur’an that He has created all things with a measure. Some
of these verses read:
[Allah has appointed a measure for all
things.]
(Qur’an,
65: 3)
[Everything has its measure with
Him.]
(Qur’an,
13: 8)
**The
author, who writes under the
pen-name Harun Yahya, has published many books
on political, faith-related and scientific issues. Some of the books of
the author have been translated into English, German, French, Spanish,
Italian, Portuguese, Albanian, Arabic, Polish, Russian, Bosnian,
Indonesian, Turkish, Tatar, Urdu and Malay and published in the
countries concerned. Visit his website at www.harunyahya.com
or contact him at info@harunyahya.com
[1]
Mehmet Suat Bergil, Doğada/Bilimde/Sanatta, Altın Oran (The
Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd
Edition, 1993, p. 155.
[2]
Guy Murchie, The
Seven Mysteries of Life, First Mariner Boks,
New York, pp. 58-59.
[3]
J. Cumming, Nucleus: Architecture and Building Construction, Longman, 1985.
[4]
Mehmet Suat Bergil, Doğada/Bilimde/Sanatta, Altın Oran (The Golden Ratio in
Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p.
87.
[5]
A. L. Goldberger, et al., “Bronchial Asymmetry and Fibonacci
Scaling.” Experientia, 41 :
1537, 1985.
[6]
E. R. Weibel, Morphometry of the Human Lung, Academic Press, 1963.
[7]
William Charlton, Aesthetics: An Introduction, Hutchinson University Library, London,
1970.
[8]
“The ‘Golden’ spirals and ‘pentagonal’ symmetry in the alive
Nature,” online at: http://www.goldenmuseum.com/index_engl.html
[9]
D’Arcy Wentworth Thompson, On
Growth and Form, C.U.P., Cambridge, 1961.
[10]
C. Morrison, Along The Track, Withcombe and Tombs, Melbourne.
[11]
“The ‘Golden’ spirals and ‘pentagonal’ symmetry in the alive
Nature,” online at: http://www.goldenmuseum.com/index_engl.html
[12]
Emre Becer, “Biçimsel Uyumun Matematiksel Kuralı Olarak, Altın
Oran” (The Golden Ratio as a Mathematical Rule of Formal Harmony), Bilim
ve Teknik Dergisi (Journal of Science and Technology), January 1991,
p.16.
[13]
V.E. Hoggatt, Jr. and Bicknell-Johnson, Fibonacci
Quartley, 17:118, 1979.
The
works posted on this page reflect solely the opinions of the authors.
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