Research Task: The Golden Section

Updated: Aug 31

For this area of research I looked into instances of the Golden section as it appears in nature, design and artwork, including where can be implemented in book design to create effective layouts. I've seen the famous spiral grid overlay used to analyse and create work in the art and illustration world before, but I was curious learn more about its origin and use in graphic design too.


The Golden Ratio


The Golden section, also known as the Golden ratio or the Golden mean, is a mathematical equation that can be used to form an image with proportions that the human eye finds naturally pleasing. A 'perfect' rectangle can be formed by halving any square, then linking together the two shapes to form a new rectangle with an aspect ratio of 2:3.

“To form a golden section rectangle from a square, the square is divided in half. The diagonal of the half square is rotated to the horizontal, defining the length of the rectangle.”

- Andrew Haslam, Book Design, 2006.

Examples of how a rectangle can be made using the golden ratio.

This pattern can then be repeated infinitely within itself, where the geometry of intersecting lines and shapes can be used to demonstrate a spiral effect. This also links together with the Fibonacci sequence of numbers that behave in a similar pattern.

"The Golden Spiral" using numbers from the Fibonacci sequence

Common Appearances


In natural forms


The golden ratio has been found to appear naturally in the patterns of petals and leaves in some plants, and the structure and shape of some animals. This can be seen on the patterns of leaves and petals in flowers and the shape of invertebrate shells.

The golden spiral as it appears in natural forms.

The repetition of this same phenomenon in nature suggests that the instincts we have towards this composition has come from millions of years of adaptation to seeing this pattern occurring in our natural environment.


In Art and Architecture


Composition techniques using the golden ratio have been studied for use in the construction of art and architecture throughout ancient human history. Structures such as the Parthenon and the pyramids of Giza in Egypt both look to have followed approximations to the golden ratio.

Artwork by Leonardo da Vinci that later served as inspiration for Salvador Dali both show how they have studied using this formula as a starting composition for their work, building focal points inside the golden sections.

Using the Golden Ratio for Book Design


There is evidence that grid systems relating to the golden section have been used in book design for almost as long as the medium has existed. Inspired by the beauty of early medieval and renaissance era manuscripts, there were several designers in the 20th century that sought to rediscover what hidden methods had been used create page layouts that had the same natural harmony.


J. A. Van De Graaf reconstructed a technique believed to be the one that had been previously used. His method for geometric construction can be used to place a proportionate area within comfortable margins for the text block to inhabit. The outer margin is half of the inner and the top margin is half of the bottom, drawing the readers eyes into a comfortable position for reading.

Van De Graaf's canon of page design

The book designer Jan Tschichold later built upon these discoveries, along with observations from other experts within the field such as Raúl Rosarivo. Tschichold's own research led him to the conclusion that the 2:3 ratio was one of the most commonly used in medieval manuscripts and a key element in traditional book design, although Van De Graafs method still remains functional for any proportion of paper.

An overlay of Jan Tschichold's Golden canon with Raúl Rosarivo's 9x9 grid system.

Tschichold then asserted the importance of the 'Golden Canon' in the design world through the releases of The New typography (1928) and The Form of the Book (1979), through which he re-popularised these age old methods for use by contemporary designers who still use this structure as a guideline for some publications today.


“Though largely forgotten today, methods and rules upon which it is impossible to improve have been developed over centuries. To produce perfect books these rules have to be brought back to life and applied.”

- Jan Tschichold, The New Typography, 1928


Other Grid Layouts


I wanted to know more about how other grid systems are being used in layout design, so I researched other examples in addition to the golden ratio. Below are images showing the types of grids mentioned in Ellen Lupton's Thinking With Type, where she gives an overview of some of the industry standard structures for layouts.


Multicolumn Grid

Source: Ellen Lupton. At: www.thinkingwithtype.com/grid

This method is particularly popular for newspapers and magazines where large blocks of text can be separated into smaller sections to make the information more easily digestible. Objects can be kept in individual columns or spread across multiple, while still staying aligned and pleasing to look at.


Modular Grid

Source: Ellen Lupton. At: www.thinkingwithtype.com/grid

Following a modular grid layout allows for a lot more creativity between the pages of a single publication. Horizontal and vertical guides divide the page up into a number of equal sections of the designers choice as is shown in this 4x4 example. Any content can now be sized to fit within these boxes comfortably with plenty of choices.


Baseline grids

Source: Ellen Lupton. At: www.thinkingwithtype.com/grid

Baseline grids can be used to govern the measurements across an entire document, making sure each divided section is appropriate in relation to the leading and font size of the main body of text. The horizontal divisions create lines for the text to sit on in the same way as we write on lined paper to keep our handwriting in line and baseline grids can be used in combination with any of the other grid systems to maintain a consistent structure.



Learning about grids has been really interesting so far and I'm looking forward to carrying on looking at layouts to see how I can use them in my own work. Applying page elements to grid systems like these will give me plenty of options for objects to have a natural relationship to each other, but it's also important for to remember that no grid layout is one-size-fits-all pathway to good design.


An appropriate grid system gives a strong starting point to work with, but a good designer still has to adapt a layout to find a composition of content that feels 'right' in the context of any given project. This can be done by both confirming to the grid and through deliberately bending and breaking some of the structural rules of the rest of the page to draw attention to an area, which is what I will be looking at in the next exercise.

Bibliography


How To Draw And Use Grid Systems In Your Design Layout (Van de Graaf Canon) (2020) [Online Video] At: https://www.youtube.com/watch?v=05gjaM5fONU


Lumpton, E. (2021) Grid At: http://thinkingwithtype.com/grid/ (Accessed 20/8/21)


Retinart. (2021) The Secret Law of Page Harmony At: https://retinart.net/graphic-design/secret-law-of-page-harmony/ (Accessed 20/8/21)


Velarde, O. (2020) A Quick Look at Types of Grids for Creating Professional Designs At: https://visme.co/blog/layout-design/ (Accessed 20/8/21)


Wikipedia. (2021) Golden ratio At: https://en.wikipedia.org/wiki/Golden_ratio (Accessed 20/8/21)


Wikipedia. (2021) Canons of page construction At: https://en.wikipedia.org/wiki/Canons_of_page_construction (Accessed 20/8/21)


Wikipedia. (2021) Fibonacci number at: https://en.wikipedia.org/wiki/Fibonacci_number (Accessed 20/8/21)