The Mihir Chronicles

Geometry Of Design | Studies In Proportion And Composition by Kimberly Elam

October 15, 2022

I. Brief Summary

A visual analysis of how design works based on mathematical foundations— golden section, root rectangles, ratios, proportions and Fibonacci Series. Kimberly takes her readers on geometrical journey by exploring visual relationships such as proportions and compositions. A short little book on how design process encompasses these geometric systems.

II. Big Ideas

  • It has technical information such as all the diagrams of golden rectangles, circles, and then there are the ratios and analysis of artworks, and even furniture and architecture and other things.
  • The numbers 8 and 13 as found in the pine cone spiral and 21 and 34 as found in the sunflower spiral are very familiar to mathematicians. They are adjacent pairs in the mathematical sequence called the Fibonacci sequence. Each number in the sequence is determined by adding together the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55....The ratio of adjacent numbers in the sequence progressively approaches golden section proportions of 1:1.618.
    • Many fish also show relationships with the golden section. And so does human body and old architectural buildings including Cathedral churches.
  • The golden section rectangle is a ratio of the Divine Proportion. The Divine Proportion is derived from the division of a line segment into two segments such that the ratio of the whole segment, AB, to the longer part, AC, is the same as the ratio of the longer part, AC, to the shorter part, CB. This gives a ratio of approximately 1.61803 to 1.
  • The special proportioning properties of the golden section have a close relationship to a sequence of numbers called the Fibonacci sequence, named for Leonardo of Pisa who introduced it to Europe about eight hundred years ago along with the decimal system. This sequence of numbers, 1, 1, 2, 3, 5, 8, 13, 21, 34... is calculated by adding the two previous numbers to produce the third.

III. Quotes

  • The purpose of Geometry of Design is not to quantify aesthetics through geometry but rather to reveal visual relationships that have foundations in the essential qualities of life such as proportion and growth patterns as well as mathematics. Its purpose is to lend insight into the design process and give visual coherence to design through visual structure. It is through this insight that the artist or designer may find worth and value for themselves and their own work.
  • The power of the golden section to create harmony arises from its unique capacity to unite different parts of a whole so that each preserves its own identity, and yet blends into the greater pattern of a single whole. — Doczi
  • Le Corbusier's revelation is one that is of value for all artists, designers, and architects. The understanding of the underlying organizational principles of geometry brings to a creative work a sense of compositional cohesiveness, whereby each element of the work has a visual sense of belonging. By revealing some of the geometry, systems, and proportions it is possible to understand better the intent and reasoning of a number of designers and architects. It gives insight into the process of realization and a rational explanation for many decisions, whether the use of organizational geometry is intuitive or deliberate, rigidly applied or casually considered.