What is the Golden Ratio?
Two objects are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The value this works out to is usually written as 1.6180. It is a mathematical ratio that is commonly found in nature, and when used in design, it fosters organic and natural looking compositions that are aesthetically pleasing to the eye. The most famous application of the golden ratio is the socalled golden rectangle, which can be split into a perfect square, and a smaller rectangle that has the same aspect ratio as the rectangle it was cut away from. One can apply this theory to a larger number of objects by similarly splitting them down.
This harmony and proportion of the golden ratio has been observed for thousands of centuries: from the Pyramids in Giza to the Parthenon in Athens; from Michelangelo’s The Creation of Adam on the ceiling of the Sistine Chapel to Da Vinci’s Mona Lisa; and from the Pepsi logo to the Twitter logo.
What is the value and how was it deduced?
The value of 1.618, mathematically irrational number is interestingly considered to be the golden ratio, golden mean, divine proportion and many other names that golden ratio is associated with. It was deduced from the Fibonacci series, which is a series of numbers in which each number ( Fibonacci number ) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc.
Golden Ratio and Design
Golden Ratio finds huge application in print design like : posters, marketing materials, visiting cards etc.
1. Golden Shapes for use
The most used golden shapes in design are Golden Rectangles, Golden Circles, Golden Spiral and Golden Triangles. Many a times, these are used in combination to create mesmerising design compositions.
2. Setting Layout dimensions with Golden Ratio
Layout in web or graphic design is used to arrange visual elements on a page. It involves organising the art composition to achieve specific communication objectives. Golden Ratio can be used here to define the widths of panels, sidebars or even height of the views. For example, layout of width 960px. Dividing this by 1.618 approximately gives us 594px (593.325..) which can very well be defined as the height of your view. Two separate sections can also be made of sizes 594px and 366px(960–594) which can form two sections page layout. We can go further dividing the space in golden mean to achieve more grids. Defining the height of any view is very prominent in Graphic design as compared to Web design since content is the factor that decides the height of the page in web design.
3. Defining spacing between content using Golden Ratio
Moving on from standard padding and margin to define the gutters and spacing between the content blocks irrespective of what the layout sizes are. Management of these positive spaces or negative spaces often make or break the final result. However, one can make use of golden rectangles to ensure that the interlayout spaces are proportional and calculated.
4. Using Golden Ratio in Typography
It can be used in figuring out the sizes of different text hierarchies in your design composition, and also used as a guide to determine the best size for each of them. Let us say body text is 10px. Multiplying it by 1.618 you have 16.18. The heading text size can be 16px. Using golden ratio simplifies the decision in determining the sizes for text hierarchy.
5. Icon/Logo design using Golden Ratio
Golden Shapes like triangles, squares, circles and spirals are widely used while designing an icon or logo. Proper use of the golden shapes can harness a proper balance and can turn a good design to a great one. We will not get into a lot of details of this section since this entirely is a larger section in its own.
Appearance of the Golden Ratio in our everyday lives:
The Golden Ratio seen in Music
Much of the rhythm and movement and design of our bodies and normal everyday life experiences all tie in with the Golden Ratio, how we perceive an object and whether we find it pleasing all goes back to the Golden Ratio. Because it is the one of the universal constants that allow for the interactions between all things on earth, it continues to hold relevance in our lives, regardless of the advancements in technology, which in fact is actually discovering more and more how life and design is so intimately associated with the Golden Ratio.
Architectural evidence of the Golden Ratio
Take a look at modern architecture and you will soon realize that the last decades have produced an increasing number of buildings with exotic shapes. Of course, also in earlier times the design of buildings has been influenced by mathematical ideas regarding, for instance, symmetry. Both historical and modern developments show that mathematics can play an important role, ranging from appropriate descriptions of designs to guiding the designer’s intuition.
Here are some of the basic examples which we encounter in our daily life:

Flower petals number of petals in a flower is often one of the following numbers: 3, 5, 8, 13, 21, 34 or 55. For example, the lily has three petals, buttercups have five of them, the chicory has 21 of them, the daisy has often 34 or 55 petals, etc.

Faces Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself.

Body parts The Golden Section is manifested in the structure of the human body. The human body is based on Phi and the number 5.The number 5 appendages to the torso, in the arms, leg and head. 5 appendages on each of these, in the fingers and toes and 5 openings on the face. Animal bodies exhibit similar tendencies.

Seed heads Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.

Fruits, Vegetables and Trees Spiraling patterns can be found on pineapples and cauliflower. Fibonacci numbers are seen in the branching of trees or the number of leaves on a floral stem; numbers like 4 are not. 3’s and 5’s, however, are abundant in nature.

Shells Snail shells and nautilus shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider’s webs.

Spiral Galaxies Spiral galaxies are the most common galaxy shape. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees.

Hurricanes It’s amazing how closely the powerful swirls of hurricane match the Fibonacci sequence.

DNA molecules The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.
Conclusion
Mathematically golden ratio is an irrational number, which means we can never achieve it perfectly in design; a debate going on for centuries.
Takeaway for designers is, use of golden ratio is not something that will make or break your designs. Not every design composition can be derived using golden ratio. If needed, it must be used as a guide to create proportions in our design. Use of golden ratio in design needs a lot of understanding and practice to perfect it. Golden Ratio is thus one more useful tool that should be there in designer’s toolbox.
However, since these are the patterns that exist in very nature around us, use of golden ratio in artistic composition brings in a natural balance and visual harmony, thereby giving an undeniable aesthetic appeal.