# 13 Real-life Examples of the Golden Ratio You'll Be Happy to Know

The golden ratio is derived from the Fibonacci sequence, and is seen universally in varied natural elements. It is a part of the natural dimensions of most biological as well as non-biological entities on this planet.

Komal B. Patil

Last Updated: Mar 26, 2018

*"Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."*

―Johannes Kepler

Golden Ratio Representation

The elucidation of the relationship between the golden section and the Fibonacci sequence is vital in order to detect and identify the presentation of this particular ratio in nature.

Real-life Examples of Golden Ratio

Flower Petals

In almost all flowering plants, the number of petals on the flower is a Fibonacci number. It is extremely rare for the number of petals not to be so. Examples of this phenomenon are: Corn marigold, cineraria, and daisies have 13 petals; asters and chicory have 21 petals; plantain and pyrethum flowers have 34 petals, etc. The golden ratio is seen in these flowers in terms of petal arrangement. All the petals exhibit a twisting of about 1.618034°, in order to optimize exposure to sunlight.

Also, flowers with multiple layers of petals exhibit the Fibonacci sequence per layer, and the top view of the flower presents the Fibonacci spiral. The ratio of petals between each layer is the golden ratio. The same is also true for the leaf arrangement of most plants

Also, flowers with multiple layers of petals exhibit the Fibonacci sequence per layer, and the top view of the flower presents the Fibonacci spiral. The ratio of petals between each layer is the golden ratio. The same is also true for the leaf arrangement of most plants

Seed Heads

Spiraling patterns of seed heads, as seen in case of sunflowers, are a great example of the Fibonaccian process and the divine ratio. In a seed head, typically, new seeds are formed at the center, and they migrate outwards in a radial fashion as they grow older. Since each whorl of the seed heads follow the sequence, it logically follows that the ratio of any two adjacent whorls is the golden ratio. The seed heads also exhibit two distinct radial orientations. If he number of total seed heads oriented in the two directions are compared, they yield the divine proportion.

Pine Cones

Similar to the spiral patterns of the seed heads, the pods of the pine cone are also arranged in a Fibonaccian spiral. Each cone consists of pairs of alternating whorls, each oriented in the opposite direction to the other whorl. The ratio of the turn of each pod and the ratio between the number of pods in successive whorls is the golden ratio, i.e., 1.618.

Branching Pattern in Trees

When the main trunk of a tree branches out, it gives rise to a side-branch, which will further go on to divide and produce two more branches. One of these branches will split and form two new growth points, while the other branch remains dormant. This occurs at each branching event along the length of the tree over the course of its lifetime. This gives rise to branches, whose number follow the Fibonacci progression. This implies that, at each branching node, the ratio of new branches to old is 1.618.

Shells

The outer calcareous shell in the case of snails, seashells, and other such examples, also exhibit the Fibonacci spiral. Snail and nautilus shells are obvious examples, where the spiral is plainly observable. Each chamber of the nautilus, when compared to its immediate successor, reveals the golden ratio. The same is true in case of snails. In case of bivalve type clams, which exhibit grooves on their shells, the ratio of the grooves to the ridges equals the golden mean. The same phenomenon is also seen in the case of horns of rams and goats, the shape of certain spider webs, and the inner cochlea of the ear.

Spiral Galaxies

The Fibonaccian spiral is also observed in case of a spiral galaxy. Our own galaxy―the Milky Way―is one such celestial entity. Certain other entities within the galaxy also exhibit the golden ratio. It is found in the ratio of the diameters of Saturn and its rings. It is also the ratio of the distances of Venus and the Earth from the Sun. Interestingly, the ratio of the revolutions of these two planets also yields the golden ratio.

Hurricanes

As in the case of shells and spiral galaxies, the movement of air and wind in hurricanes also follows the Fibonaccian spiral, revealing the golden ratio. The spiral nature of a hurricane is largely due to the simultaneous movement of the air and atmospheric elements between a low pressure area (epicenter of the hurricane) and the surrounding high pressure area.

► Outer and inner edge of the eye ● Center of the nose

► Outer edges of the lips ● Upper ridges of the lips

► Width of the center tooth ● Width of the second tooth

► Width of the eye ● Width of the iris

Reproduction Dynamics

In honeybee populations, the ratio of females to males is 1.618. Also, according to bee reproduction, fertilized eggs become female bees, whereas the unfertilized ones become males. Therefore. The females possess two parents, while the male only possesses one parent. Hence, if one were to examine the family tree of individual bees, the number of parents would progress from the newest to the oldest in a Fibonacci sequence.

Animal Bodies

Animals show a wide range of body structures. Despite this vast range, they still exhibit the divine proportion in various parts of their bodies. Some examples include:

► Dolphins: Dimensions (length:breadth) of eyes, fins, as well as tail section.

► Penguins: The ratio of the position of the body markings at the eyes, beak, and wings, in contrast with its total height.

► Tiger: Almost all the facial features and their positions show golden sections, including the ratio of the length and breadth of the face.

► Insects: The ratios of the body segments (head, thorax, and abdomen) to each other are golden sections.

► Dolphins: Dimensions (length:breadth) of eyes, fins, as well as tail section.

► Penguins: The ratio of the position of the body markings at the eyes, beak, and wings, in contrast with its total height.

► Tiger: Almost all the facial features and their positions show golden sections, including the ratio of the length and breadth of the face.

► Insects: The ratios of the body segments (head, thorax, and abdomen) to each other are golden sections.

Human Bodies

Golden ratios that are observed in the human body are as follows:

► Head to toe ● Head to navel

► Ratio of the length of each digit of a finger

► Shoulder to fingertip ● Shoulder to elbow

► Hip bone to heel ● Hip bone to knee

► Chest length ● Waist length

► Head to toe ● Head to navel

► Ratio of the length of each digit of a finger

► Shoulder to fingertip ● Shoulder to elbow

► Hip bone to heel ● Hip bone to knee

► Chest length ● Waist length