Thursday, July 21, 2011

The Measure of Beauty Created in Nature: The Golden Ratio

Semalam (20/7/2011) saya berada di Kem Intan Suraya, Sungai Siput, Perak bersama team AASB mengendalikan training Program Transformasi Modal Insan. Bilangan peserta yang hadir lebih kurang 60 orang. Persekitaran kem ini amat menarik ditambah dengan kedudukannya yang bersebelahan dengan sungai Perak. Suasana alam dan ikan-ikan sungai yang bermain di tebing membangkit rasa ketenangan dalam jiwa.

Apa yang ingin saya kongsikan di sini ialah mengenai satu pengetahuan baru yang saya perolehi semasa di kem tersebut. Haji Mohd Ghozali atau Pak Malim, seorang penceramah yang dijemput oleh penganjur telah berkongsi dalam ceramah beliau berkaitan GOLDEN RATIO. Beliau menerangkan kaitan sains dengan al-Quran dari sudut pandang ilmu matematik. Pada mulanya, agak susah untuk memahami apa yang beliau sampaikan kerana saya kurang mendalami ilmu matematik. Namun, saya tetap cuba untuk memahami dan mencari pengertian di sebalik apa yang disampaikan. Saya juga menyalin beberapa keywords untuk membantu memudahkan rujukan melalui buku atau internet. Keterbatasan sesi selama 1 jam itu tidak memungkinkan saya untuk memahami dengan jelas. Justeru, saya telah membuat sedikit rujukan dan pembacaan serta rasa elok ia dikongsi bersama.

Jadi untuk membolehkan perkongsian yang lebih meluas, saya telah merujuk pada laman web Harun Yahya mengenai tajuk ini. Di bawah ini adalah petikan langsung dari laman web tersebut:

The Measure of Beauty Created in Nature:
The Golden Ratio


Allah has appointed a measure for all things. (Surat at-Talaq, 3)

… You will not find any flaw in the creation of the All-Merciful. Look again-do you see any gaps? Then look again and again. Your sight will return to you dazzled and exhausted! (Surat al-Mulk, 3-4)

... 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)
L. Pisano Fibonacci

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 in the series. This number is known as the "golden ratio."


233 / 144 = 1.618

377 / 233 = 1.618

610 / 377 = 1.618

987 / 610 = 1.618

1597 / 987 = 1.618

2584 / 1597 = 1.618


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 "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 in the table below 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.


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.

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. (18)


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.

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. (Surat at-Talaq, 3)

… Everything has its measure with Him. (Surat ar-Ra'd, 8)

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