The Golden Ratio
Allah has appointed a measure for all things. (Surat atTalaq, 3)
… You will not find any flaw in the creation of the AllMerciful. Look againdo you see any gaps? Then look again and again. Your sight will return to you dazzled and exhausted! (Surat alMulk, 34)
... If a pleasing or exceedingly balanced form is achieved in terms of elements of application or function, then we may look for a function of the Golden Number there ... 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 do 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)
Leonardo Fibonacci 
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 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 HUMAN BODY AND THE GOLDEN RATIO
Leonardo da Vinci used the golden ratio in setting out the proportions of the human body 
THE GOLDEN RATIO IN THE HUMAN BODY
The M/m level in the table below is always equivalent to the golden ratio. M/m = 1.618
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
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
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
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 whose sides are 1.618 and 1 units 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. The first examples we can give of this are the spiral sequences on the sunflower and the pine cone. In addition to this, an example of Almighty Allah's flawless creation and how He has created everything with a measure, the growth process of many living things also takes place in a logarithmic spiral form. The curves in the spiral are always the same and the main form never changes no matter their size. No other shape in mathematics possesses this property. (8)
The Design in Sea Shells
The flawless design in the nautilus shell contains the golden ratio 
When investigating the shells of the living things classified as mollusks, which live at the bottom of the sea, the form and the structure of the internal and external surfaces of the shells attracted the scientists' attention:
The internal surface is smooth, the outside one is fluted. The mollusk body is inside shell and the internal surface of shells should be smooth. The outside edges of the shell augment a rigidity of shells and, thus, increase its strength. The shell forms astonish by their perfection and profitability of means spent on its creation. The spiral's idea in shells is expressed in the perfect geometrical form, in surprising beautiful, "sharpened" design. (9)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 a superior intellect and knowledge, and belongs to Almighty Allah, the Creator of all things:
"My Lord encompasses all things in His knowledge so will you not pay heed?" (Surat alAn'am, 80)
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 motherofpearl lined walls. As the animal grows, it builds another chamber at the spiral shell mouth larger than the one before it, and moves forward into this larger area by closing the door behind it with a layer of motherofpearl. (11)
The scientific names of some other marine creatures with logarithmic spirals containing the different growth ratios in their shells are:
Haliotis Parvus, Dolium Perdix, Murex, Fusus Antiquus, Scalari Pretiosa, Solarium Trochleare.
Ammonites, extinct sea animals that are today found only in fossil form, too, had shells developing in logarithmic spiral form.
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. (12)
The Golden Ratio in the Hearing and Balance Organ
Horns and Teeth That Grow in a Spiral Form
THE GOLDEN RATIO IN THE MICRO WORLD
Threedimensional forms that contain the golden ratio are very widespread in microorganisms. Many viruses have an icosahedron shape. The best known of these is the Adeno virus. The protein sheath of the Adeno virus consists of 252 protein subunits, all regularly set out. The 12 subunits in the corners of the icosahedron are in the shape of pentagonal prisms. Rodlike structures protrude from these corners.
The first people to discover that viruses came in shapes containing the golden ratio were Aaron Klug and Donald Caspar from Birkbeck College in London in the 1950s. The first virus they established this in was the polio virus. The Rhino 14 virus has the same shape as the polio virus.
Why is it that viruses have shapes based on the golden ratio, shapes that it is hard for us even to visualise in our minds? A. Klug, who discovered these shapes, explains:
My colleague Donald Caspar and I showed that the design of these viruses could be explained in terms of a generalization of icosahedral symmetry that allows identical units to be related to each other in a quasiequivalent way with a small measure of internal flexibility. We enumerated all the possible designs, which have similarities to the geodesic domes designed by the architect R. Buckminster Fuller. However, whereas Fuller's domes have to be assembled following a fairly elaborate code, the design of the virus shell allows it to build itself. (14)Klug's description once again reveals a manifest truth. There is a sensitive planning and intelligent design even in viruses, regarded by scientists as "one of the simplest and smallest living things." (15) This design is a great deal more successful than and superior to those of Buckminster Fuller, one of the world's most eminent architects.
The dodecahedron and icosahedron also appear in the silica skeletons of radiolarians, singlecelled marine organisms.
Structures based on these two geometric shapes, like the regular dodecahedron with feetlike structures protruding from each corner, and the various formations on their surfaces make up the varying beautiful bodies of the radiolarians. (16)
As an example of these organisms, less than a millimetre in size, we may cite the icosahedron based Circigonia Icosahedra and the Circorhegma Dodecahedra with dodecahedron skeleton. (17)
The Golden Ratio in DNA
THE GOLDEN RATIO IN SNOW CRYSTALS
THE GOLDEN RATIO IN SPACE
The Golden Ratio in Physics
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, microorganisms, 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. (Surat atTalaq, 3)
… Everything has its measure with Him. (Surat arRa'd, 8)
1 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn 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. 5859.
3 J. Cumming, Nucleus: Architecture and Building Construction, Longman, 1985.
4 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn 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 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn Oran (The Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p. 77.
9 "The 'Golden' spirals and 'pentagonal' symmetry in the alive Nature," online at: http://www.goldenmuseum.com/index_engl.html
10 D'Arcy Wentworth Thompson, On Growth and Form, C.U.P., Cambridge, 1961.
11 C. Morrison, Along The Track, Withcombe and Tombs, Melbourne.
12 "The 'Golden' spirals and 'pentagonal' symmetry in the alive Nature," online at: http://www.goldenmuseum.com/index_engl.html
13 J. H. Mogle, et al., "The Stucture and Function of Viruses," Edward Arnold, London, 1978.
14 A. Klug, "Molecules on Grand Scale," New Scientist, 1561:46, 1987.
15 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn Oran (The Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p. 82.
16 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn Oran (The Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p. 85.
17 For bodies of radiolarians, see H. Weyl, Synnetry, Princeton, 1952.
18 Emre Becer, "Biçimsel Uyumun Matematiksel Kuralý Olarak, Altýn Oran" (The Golden Ratio as a Mathematical Rule of Formal Harmony), Bilim ve Teknik Dergisi (Journal of Science and Technology), January 1991, p.16.
19 V.E. Hoggatt, Jr. and BicknellJohnson, Fibonacci Quartley, 17:118, 1979.
2 Guy Murchie, The Seven Mysteries of Life, First Mariner Boks, New York, pp. 5859.
3 J. Cumming, Nucleus: Architecture and Building Construction, Longman, 1985.
4 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn 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 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn Oran (The Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p. 77.
9 "The 'Golden' spirals and 'pentagonal' symmetry in the alive Nature," online at: http://www.goldenmuseum.com/index_engl.html
10 D'Arcy Wentworth Thompson, On Growth and Form, C.U.P., Cambridge, 1961.
11 C. Morrison, Along The Track, Withcombe and Tombs, Melbourne.
12 "The 'Golden' spirals and 'pentagonal' symmetry in the alive Nature," online at: http://www.goldenmuseum.com/index_engl.html
13 J. H. Mogle, et al., "The Stucture and Function of Viruses," Edward Arnold, London, 1978.
14 A. Klug, "Molecules on Grand Scale," New Scientist, 1561:46, 1987.
15 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn Oran (The Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p. 82.
16 Mehmet Suat Bergil, Doðada/Bilimde/Sanatta, Altýn Oran (The Golden Ratio in Nature/Science/Art), Arkeoloji ve Sanat Yayinlari, 2nd Edition, 1993, p. 85.
17 For bodies of radiolarians, see H. Weyl, Synnetry, Princeton, 1952.
18 Emre Becer, "Biçimsel Uyumun Matematiksel Kuralý Olarak, Altýn Oran" (The Golden Ratio as a Mathematical Rule of Formal Harmony), Bilim ve Teknik Dergisi (Journal of Science and Technology), January 1991, p.16.
19 V.E. Hoggatt, Jr. and BicknellJohnson, Fibonacci Quartley, 17:118, 1979.
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