An Introduction to the Amazing Golden Ratio and the Fibonacci Sequence

Sacred Geometry, Phi, and the Golden Ratio

Sacred geometry refers to shapes and patterns that are thought to have spiritual, symbolic and sacred meanings with identifiable geometric proportions, and their related spiritual study.

The Fibonacci sequence is a series of numbers starting from 0, 1, 1, 2, 3, 5, 8, 13, 21, 43, 55, 89, 144, 233, 377 and so on. Each number is the sum of the two preceding numbers.

The ratio or relationship of two neighboring Fibonacci numbers is a known as the Golden Ratio, 1.618, represented by the Greek letter ‘phi’ ‘Φ’ and its inverse 0.618. It is also known as the golden mean, golden section, divine proportion and golden ratio, first mentioned by the Greek mathematician, Euclid.

This also represents one of sacred geometry’s key elements, displaying a symmetrical relationship, or ratio, between the small and larger parts is equal to that between the whole and larger part, in this case, the ratio of 1:618.

The pattern of the ratio is simple but appears like a built-in numbering system composition to the cosmos, as seen in patterns of galaxies, flowers, hurricanes, sea shells and more. The mathematical ratio can be found everywhere in nature and creates pleasing, organic compositions in artwork and design projects. Its emergent patterns and ratio are all over from micro to macro scale and biological systems to inanimate objects.

Mathematicians have spent endless hours in finding this simple ratio and its properties that thinkers of all other disciplines got inspired including musicians, psychologists, biologists, architects, artists, mystics, etc. There is nothing like this research in the history of Mathematics.

The concept of the Golden Ratio is quite simple: Given two segments of a line, the shorter segment is given a length of 1, and the remaining segment is roughly 1.618 times the length of the first segment. This ratio of 1:1.618 was used by Greek architects, incorporating its pleasing proportions and can also be found in nature.

Fibonacci Sequence and the Golden Ratio
This essence of the Golden Ratio and Fibonacci Sequence: 1 is the short segment, 1.618 is the length of the longer segment, where each segment in the sequence is 1.168 larger than the previous.

Where is the Fibonacci Sequence/Golden Ratio found in Nature?

Fibonacci sequence / the golden ratio is everywhere in the universe. Let’s find out where.

Golden Ratio and the Human Body

Given a length of 1 to the human arm, from shoulder to elbow, the length from the elbow to the longest finger tip is typically 1.168 times that length. Therefore, a 1:1618 ratio.

The Golden Ratio superimposed on the human arm

In reference to anatomy, the Golden Ratio can be seen in several seen in the human body from the navel to the floor and from the top of the head to the navel.

1 (small) 1.618 (larger)
Forehead to eye
Middle of mouth to bottom of nose
Eye to chin
Middle of mouth to chin

Golden Ratio in Flower Petals

The number of petals in a flower has the Fibonacci sequence. Like three petals in lily, five petals of buttercups flower, daisy have 34 petals whereas chicory has 21. The number of petals is based on Phi’s appearance in the packing arrangement of the flower. It is placed at 0.618034 (the reciprocal of 1.618…) per turn so the best possible sunlight exposure can be given to them.

Golden Ratio and Flowers

The head of the flower is also according to the Fibonacci sequence. It starts producing at the centre and fills the space to give support and contributions to gloom the flower.

The Fibonacci sequence found inside a flower

The Fibonacci sequence found in rose petals

The Golden Ratio and Vegetables

The patterns shown in pineapples and cauliflower are in form of the Golden Ratio and Fibonacci sequence pineapples grow in three distinct rows of 5, 8 and 13 parallel rows.

8, 13 and 21 parallel pineapple rows, corresponding to the Fibonacci sequence, 1, 2, 3, 5, 8, 13, 21, 34, …

The Fibonacci Sequence and Tree branches

We usually see trees everywhere but never noticed the patterns in them. A Fibonacci sequence starts from the trunk then split into 2 branches and then splits into 2 another and the process continues.

Here, we can see how many branches there are at each step, counting from the ground, up, where the next number is a sum of the previous two, with the blue numbers indicating the width of each branch.

The Golden Ratio and Shells

As you many have noticed from the Golden Spiral, it looks like a shell. Shell have the unique property of the Golden Ratio in which the ratio of both sides is equal to the mean i.e. phi. It results in a nesting process of infinity and gives it a spiral form. It is also known as a logarithmic spiral that abounds in nature.

The Golden Ratio, as seen superimposed on a shell

The Golden Spiral and Spiral Galaxies

As all normally visible particles are having Fibonacci patterns, then how will our galaxies get avoided. The Milky Way galaxy has several special arms or spirals of around 12 degrees. Andromeda nebula and the Milky Way Galaxy, have spiral patterns resembling the Golden Spiral.

Hurricanes/ Storms

The storm follows o and 1 in the Fibonacci sequence. It increases in a consistent pattern and spiral of ratio.

Golden Ratio pattern of a hurricane

The Golden Ratio, Human and Non-human Faces

As mentioned above, the mouth and eyes are properly positioned at the golden sections as per the distance between the eyes and chin. These proportions can be seen from profiles, for example, the profile of the human ear.

Fibonacci Sequence and Finger Length

The length and sections of fingers from the tip to the wrist are larger than the preceding one, with the ratio of phi, the Golden Ratio.

The Golden Ratio and Fibonacci Sequence shown in the hand’s finger length.

Fibonacci, Fish and Insects

Dolphins, starfish, ants, honey bees, starfish, etc. For example, below you can see the golden ratio in the biological structure of a starfish.

Golden Ratio in the structure of a starfish

DNA Molecules

One DNA molecule measures 34 angstroms long in length and 21 angstroms in width to capture 1 full cycle of double helix spiral. So both the numbers 34 and 21 are in golden sequence and their ratio is approximately equal to phi.

The Golden Ratio and Ornaument

As mentioned earlier, ancient Greeks and modern through to modern-day artists incorporate the Golden Ratio in their designs.

As a part of our journey, we used the aesthetic appeal of the Golden Ration in the design of our very own Ornaument incense holder and further allows one to connect with infinite components of nature.

The Golden Ratio, used in the design of Ornaument

In designing Ornaument, we made careful consideration as to the placement of the Aum (om) circle. It is centered, and clearly bifurcated by the first segment of the Golden Ratio, with the over-all height and width, equally proportional to the Golden Ratio.

Another significant feature, is the incorporation of the powerful Angel Number 105, clearly depicted when incense sticks are held in place.

We welcome you to take a closer look at this beautiful piece.

Why does the Golden Ratio seem to be everywhere?

The Golden Ratio is a divine ratio. The frequent appearances or a presence of the sequence in almost everything in nature is a sign that the Fibonacci sequence work for a divine design. Some people also state that it is a signature of God in nature. So the interpretation of the golden ratio is very subjective. Some relate it with aesthetic beauty in proportions while others relate it with nature.

Do you have more examples of the Golden Ratio? Let us know in the comments!

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