Golden Section“, also known as the golden ratio, golden mean, or divine proportion, in mathematics, the irrational number (1 + √5)/2, often denoted by the Greek letters τ or ϕ, and approximately equal to 1.618 Britannica. This mathematical ratio of 1 to 1.618 (actually 1.6180339887498948482… ), is commonly found in nature. The use of the “Golden Ratio” has been widely associated with Architecture, Art, and most Design disciplines.

Golden Section common names

“Golden Ratio”, “divine proportion”, “golden mean”, “golden section”, “Fibonacci number” and “φ (phi)”

The use of the “Golden Ratio” in architecture

It is claimed that early important architectural monuments, were designed and built in accord with golden ratio rules (proportions), most notably the great pyramid of Giza, the Parthenon, Notre Dame church, the Taj Mahal, and last but not least the United Nations building in NYC by architect Le Corbusier. Whether the “Golden Ratio” was intentionally used in the creation of these early monuments, or whether it was simply good intuitive aesthetics that were put to use, is a subject for a long debate.

Divine proportions used in paintings

The Law of the Golden Section states that: “For a space divided into equal parts to be agreeable and aesthetic, between the smallest and largest parts there must be the same relationship as between this larger part and the whole space” Vitruvius (Born c. 80–70 BC, died after c. 15 BC)

Golden Ratio or as it has been coined “Divine Proportion” is closely associated with many works of art. Paintings by the old masters contain these so-called “Divine” proportions. Perhaps the most famous is Leonardo Da Vinci’s “Mona Lisa” and “The Vitruvian Man”.

Although artists are said to have used the golden mean in many parts of their painting details, the most striking perceptible visual effect is achieved when the overall dimensions of height to width is approximately 1:1.618. Following are some notable examples of paintings that have these dimensions. In all of them, the rectangles are within the “golden ratio” proportions.:

1) “The last super” – Leonardo Da Vinci
2) Parts of The Sistine chapel paintings – Michaelangelo
3) “The Dresden triptych” – Jan Van Eyck
4) “The Sacrament of the Last Supper” – Salvador Dalí
5) “Bathers at Asnières” – Georges Seurat.

When used in painting, the golden ratio is a composition strategy that is claimed to have the result of “a” or “the” most pleasing visual effect. The examples below show a painting that maintains Golden Ratio proportions, versus the resulting proportions of a digital camera photograph when the aspect ratio of 3:2 was selected. Digital camera users can choose 3:2 or 16:9 as an aspect ratio for their image captures. But, neither of the two is based on the Golden Ratio.

Creation

Golden Ratio proportions (painting)

Non Golden Ratio proportions (digital camera 3:2)

The theory in practice

The painting images below show the “Golden Ratio” overlay (left) and the “Rule of Thirds” mostly used by photographers overlay (right) with a preference for the use of the Golden Ratio. The art is a 44 x 27 inch (1:1.618 ratio) oil painting titled “The future is bright”. In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, where the relation between height and width is approximately 1.618.

In this painting, the key element of interest, a sitting person gazing at the future, was positioned in the bottom left hand side according to the “Rule of Thirds”.

Rules of Thirds and Golden Ratio overlay

Rule of Thirds overlay

Use in Book Design

Jan Tschichold who was a calligrapher, typographer and a book designer claimed that “…There was a time when deviations from the truly beautiful page proportions 2:3, 1:√3, and the Golden Section were rare. Many books produced between 1550 and 1770 show these proportions exactly, to within half a millimeter…” source (Wikipedia)

Examples found in nature

The Golden ratio is derived from the “Fibonacci sequence”, named after its’ author an Italian mathematician of the 12th century. This is a sequence of numbers that is found in nature’s creations. From the leaf arrangements in plants, to the pattern of the florets of a flower. Most notable examples of the Fibonacci number in nature, the number of petals in a flower the pine cones and shells, all show the spiral pattern. The reason for the arrangements, has most likely to do with space efficiency.

Visual presentation surfaces

Based on research it would appear that manufacturers who produce products where “visual” presentation is the main function, for the most part have not embraced the “Golden Ratio”. Popular size examples follow:
Artist material surfaces: 9×12, 12×16, 16×20, 18×24, 14×19, 22×30, 30×40, 36×48 all targeting a 1.33 ratio
Photographic paper surfaces: “A” series International 1.41 ratio source “Zabbage
Television (LCD) surfaces: 55×33, 48×28, 35×20, 43×25 between 1.67-1.72 ratio

Closest to the 1.618 ratio are the TV, LCD surfaces

The “Golden Section” versus “Rule of Thirds” debate

Artists and photographers creating “fine art”, are often debating whether it is better to apply the “Golden Ratio” or “Rule of Thirds” in their compositions. While the great masters, have used the Golden Ratio, modern day fine art photographers are mostly using the “Rule of Thirds” which is a simplified approximation of the first. Perhaps photographers are more practical and prefer simplicity and ease of use.

Digital camera manufacturers have cleverly included the “Rule of Thirds” grid as a selection option, allowing photographers to create their compositions and maintain a straight horizon line. The 3:2 ratio is standard for all 35 mm camera sensors. The other available option is the 16:9 (Sony A7r). Regrettably, neither one of these ratios, is compliant with the proportions of the Golden Section theory. So for now, those who prefer the Golden Ratio, must crop.

Digital camera 3:2 with “Golden Ratio” overlay

Digital camera 16:9 with “Golden Ratio” overlay

Conclusion

Like with most things in life, the choice is a matter of preference and there is no right or wrong. I believe, those academically inclined would rather choose “Golden Ratio” and the others most likely prefer “Rule of Thirds”. Any of the two grids below can produce wonderful results in the right hands.

The “Golden Ratio” PHI Grid

Rule of thirds grid

The “Rule of Thirds” Grid

Suggested Reading

The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number – Mario Livio, Amazon book
Da Vinci and the Divine Proportion in Art Composition – The Golden Number
Michelangelo’s Sistine Chapel frescoes linked to the golden ratio – LA Times
Why the golden ratio is better than the rule of thirds – PetaPixel
What is the Golden Ratio? – Live Science
What Is The Golden Ratio? What You Need to Know and How To Use It – Rebecca Gross, Canva Learn
Is photography art? – artgreeT Blog
How to Use the Golden Ratio to Create Gorgeous Graphic Designs – Company Folders