Check out parent post : The Golden Ratio, Fibonacci series and their applications.

**Golden ratio in Biology**

Nature too is replete with numerous examples of the Golden Ratio. Nature has followed this proportion in its own creations.

Let’s first consider the spiral structure of a snail. Do you find anything interesting? Yes, the spiral structure of the snail perfectly follows the Golden Spiral. Other examples of the Golden Spiral in animal systems include the horns of the ram, beak of the parrot, claws of the lion and many more.

In plant systems also we can find ‘mathemagic’ at work. The majority of flowers have a characteristic number of petals; these numbers are nothing but the numbers of the Fibonacci series. For example, follow the average number of petals in some common flowers: Lilies = 3, Buttercups = 5, Delphinium = 8, Marigold, Corn = 13, Chicory, Black- eyed susans = 21, Pyrethrum = 34, Sunflower, Daisies = 55/89.

Isn’t that amazing? Daisies are much more interesting, because they have been found to have different petal numbers in their flowers. The numbers are 13,21,34,55 and 89…all are Fibonacci numbers! However, due to malnutrition or defective development sometimes they may contain 33 petals.

We are more likely to notice a symmetrical body and a proportional face. We also find certain buildings and monuments more attractive than others because they have mathematical symmetry built into them.

Now, let’s take another example. The seeds of Pinecones are arranged in a spiral fashion. They contain both left- handed and right-handed spirals. If we examine carefully, we find that there are 34 right-handed and 55 left-handed spirals inside the pinecone. And, interestingly, 34 and 55 are successive numbers in the Fibonacci series!

A similar pattern is observed in the case of seeds of sunflower. Here the number of clockwise and anticlockwise spirals is 55 and 89, respectively. Again, the numbers are successive numbers in the Fibonacci series. Perhaps, the Fibonacci pattern of arrangement is the best arrangement pattern in the biological system. We find the golden ratio concept in several other plant related phenomena. Arrangement of leaves in a plant (Phyllotaxis) is governed by critical implication of the Golden Ratio, which allows best utilization of sunlight by the leaves. The role of Golden Ratio can also be found in the branching pattern of plants, if analyzed critically.

DNA (deoxyribonucleic acid), the molecule of life, is a fantastic example of Golden Ratio. The width of DNA is about 21 angstrom and height of one complete turn 34 angstrom. Again successive Fibonacci numbers! Naturally, the ratio of its height (of one complete turn) and width is a Golden Ratio.

Moreover, the right-handed spiral structure of DNA produces two grooves, known as major groove and minor groove. One major groove and one minor groove together imply a complete helical turn of DNA, which is 34 angstrom in length. Interestingly, major groove (about 21 angstrom) and minor groove (about 13 angstrom) lengths are in almost Golden Ratio (21/ 13 = 1.6153…).

**Golden Ratio in the Human Body**

Human beings are no exception to the golden ratio. In fact, our body architecture is one of the most perfect examples of this ‘Divine proportion’. Consider the following:

■ Height:length between naval point and foot

■ Length between shoulder line:length of the head

■ Length between finger tip to elbow:length between wrist and elbow

■ Length between naval point to knee: length between knee and foot

Just measure these lengths and try to find out the ratio. All the ratios are very close to the Golden Ratio.

Curiously enough, you also have 2 hands, each with 5 digits, and your 8 fingers are each comprised of 3 sections. All Fibonacci numbers!

Each section of your index finger, from the tip to the base of the wrist, is larger than the preceding one by about the Fibonacci ratio of 1.618, also fitting the Fibonacci numbers 2, 3, 5 and 8. By this scale, your fingernail is 1 unit in length.

Your hand creates a golden section in relation to your arm, as the ratio of your forearm to your hand is also 1.618, the Divine Proportion.

In our face golden ratios are found in abundance. For example, length of the face: width of the face; length of mouth: width of nose; width of nose: length between nostrils; length between pupils: length between eyebrows. The proportions are not constant in all individuals. But, in a perfect and so- called beautiful face, all these proportions are close to the Golden Ratio. The golden ratio thus gives us a mathematical definition of ‘beauty’.

It is often believed that magic starts where mathematics ends. But we find some mysteries that lie at the junction of these two most amazing fields. Perhaps the golden number is one of such mysteries. It should be considered as the link between mathematics and our magical nature. Several attempts are being taken to decipher as well as mimic nature’s definition of beauty via the golden proportion. The concept is being employed in modern designing and architecture.

Also read : Applications of golden Ratio in Ancient Arts and Architecture

thank you for your help