A is to B as B is to A + B

The Golden Mean


 

Introduction:

I was entranced by the myth of the artist when I was a teenager. As I began to read about the history of western art I kept bumping into mysterious phrases like "Golden Mean," "Golden Proportion," "Golden Rectangle," and "Golden Section." I was certain that there must be some great mystery of the universe revealed in this mysterious sounding concept. Why else was there so much talk about it? But even though I heard it frequently mentioned or saw examples of its use in the compositions of the old masters, it was never clear to me just why it was such a big deal.
 
    It was not until many years later when I learned about Fibonacci Numbers and their relationship to the Golden Section that it started to come together for me. It was when I was well into the work on the triptychs at NFMOA that I realized how the Golden Proportion is within us and around us everywhere!
 
    The Third Triptych at NFMOA, "The East," is based on the Golden Proportion and the Fibonacci Numbers. Photographs and more information about "The East" triptych, are presented on the Full Tour.
 
    For centuries, artists, architects and engineers have studied and used the Divine Equation, as the ancient Egyptians referred to it. It is inherent in the structure of flora and fauna as well as in mathematics. The anatomy of human beings is full of Golden Sections. Every time I glance at my hand I see the Divine Equation!
 
    The very fact that it is such an integral part of the physical and natural world is perhaps why we respond so positively when we see it being used in art and architecture.  

 

A:B=B:A+B

This formula may look a bit imposing. But it doesn't sound quite so strange as it looks. If you ask a mathematician to read it aloud, this is what you will hear: " A is to B as B is to A plus B."
 
    What it means is that whenever the length of "A" in relation to "B" is the same as the relation of "B" is to the length of "A" and "B" put together, the Golden Section is present. If it is still a bit confusing examine the illustration at the top of this page or take a look at the Golden Section in the Human Hand in the Resources section below.
 
 

The Golden Section Tool

One way to begin to appreciate the Golden Proportion is to observe it in our own bodies and in the world around us. I use a simple tool to discover the Golden Proportion in the world and to create the Golden Section whenever I need it in my painting or sculpture. Complete instructions and diagrams have been included to help you make your own Golden Section Tool.
 

 

Resources

Make Your Own Golden Section Tool
Photo, diagrams and complete instructions for an inexpensive and easy-to-make tool.

The Golden Section in the Human Hand
A photograph of the author's hand revealing a couple of the many instances of the Golden Section in human anatomy.

Fibonacci and the Golden Mean
Some very useable and easily understood explanations of Fibonacci numbers and the Golden Mean.

The Human Side: IMPROVING DESIGN WITH HUMAN PROPORTIONS
Concise discussion of the need for acknowledgement of human proportions in the design of products and places in our world.
 
The Golden Mean
Clear and easy to understand diagrams, explanations and math related to the Golden Mean and Fibonacci numbers.

The Power of Limits: Proportional Harmonies in Nature, Art and Architecture
A great book with wonderful illustrations, by Gyorgy Doczi, Shambala, 1981
 
 
 

Fibonacci Numbers

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, etc.
 
(Each number is the sum of the previous two numbers. Except for the number 1, any two adjacent numbers in the series, when seen as a ratio, are very close to the Golden Mean: 89/144= 0.61805555556; when seen as fractions, they make it easy to remember how to create or identify the Golden Section: 2/3, 5/8, 8/13, etc. )
 

 
Golden Proportion and linked pages:
© R. Comings 1998-2011

 
 

Tool Description and Instructions

How to Create the Golden Section
 
 
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