In simple terms, if two rectangles are in the golden section then the same ratio will be found when the sum of the parts are compared to the larger original part. This ratio is 1.618. The diagram below illustrates the point:
If you pay attention to the rectangles you will see how this ratio can continue ad infinitum. This can be described mathematically as (a+b is to a as a is to b). This consistent relationship between the rectangles also creates a spiral that can be seen in the diagram above. This also relates to the mathematical Fibonacci sequence where each number is the sum of the two preceding numbers, for example, the first 12 numbers in the sequence are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
The golden ratio is expressed in nature in myriad ways:
It can also be seen in many examples of art:
There is something inherently pleasing about the golden ratio and the proportions and composition it supports.
Book Design
A Dutch book designer called J. A. van de Graaf created a formula for page format after looking at medieval manuscripts and noticing many had similar layouts. The end result is an area for text that is surrounded by an inner margin of 1/9 and an outer margin of 2/9. The bottom margin is also double that of the top margin, with the top margin being 1½/9 and the bottom margin being 3/9. The Gutenberg Bible featured below is a famous example of this.
Jan Tschichold was another designer who noticed that the golden section had been used in the history of book design.
The above diagram illustrates Tschichold’s analysis of medieval manuscripts with this example featuring a 2:3 ratio and margin proportions of 1:1:2:3 which are Fibonacci numbers. The golden ratio is 1.618 and can be found in the A format sizing for books in the UK as well as approximate matches with many other formats.
References
Wikipedia. 2020. Canons of page construction. [ONLINE] Available at: https://en.wikipedia.org/wiki/Canons_of_page_construction. [Accessed 28 August 2020].
Daniel's OCA Blog: Book Design 1 
