Monday, January 17, 2011

The Mysterious Golden Ratio

  Émilie du Châtelet-Sheva Apelbaum

The golden ratio, also known as Phi (symbol \varphi \, or\Phi \, ), is a numerical constant that equals approximately 1.61803398... Interestingly, the inverse of Phi (1/Phi) equals (Phi-1) or 0.61803398... 

There are many ways to calculate the golden ratio. I have included three easy ones in this spreadsheet.   I first discovered Phi when my dad told me about a number sequence called Fibonacci (I’ll write more about this interesting sequence in a future posting).

One of the interesting things about the golden ratio is that it can be found everywhere around us, if you know where to look. You can find it in nature, art, design, architecture, and math.  To help search for the ratio, I built a special gauge (with little help from my dad).  I can check for the golden ratio by simply placing the gauge over an item and extending it until it fits. 
  Golden Ratio Gauge-Sheva Apelbaum 
After walking around inside the house and outside for about an hour, I discovered dozens of examples.  As you can see from the few illustrations below, it’s really easy to find them once you know what to look for. 

In our bodies:
Golden Ratio Body-3-Sheva Apelbaum Golden Ratio Body-2-Sheva Apelbaum
 Golden Ratio Body-6-Sheva Apelbaum Golden Ratio Body-4-Sheva ApelbaumGolden Ratio Body-8-Sheva Apelbaum Golden Ratio Body-7-Sheva Apelbaum

In architecture (King Solomon's Temple):
Golden Ratio Architecture-2-Sheva Apelbaum Golden Ratio Architecture-1-Sheva Apelbaum 
Golden Ratio Architecture-3-Sheva Apelbaum

In art:
Golden Ratio Art-3-Sheva Apelbaum Golden Ratio Art-1-Sheva Apelbaum  
Golden Ratio Art-4-Sheva Apelbaum Golden Ratio Art-2-Sheva Apelbaum

In design:
Golden Ratio Design-3-Sheva Apelbaum Golden Ratio Design-2-Sheva Apelbaum Golden Ratio Design-6-Sheva Apelbaum Golden Ratio Design-4-Sheva Apelbaum 

In nature:
Golden Ratio Nature-1-Sheva Apelbaum
Golden Ratio Nature-2-Sheva Apelbaum

It is interesting how common the golden ratio is.  It is also interesting to see how often it’s used in our daily life.  For some reason, we chose it instinctively and we consider it “attractive”.  When I asked my mom why she placed the handle on her mugs using the specific proportions  that she does (see mug below), she said that she did not know, that it just felt “right”.  

Golden Ratio Design-5-Sheva Apelbaum

Perhaps beauty is not a personal preference after all. Maybe what most of us consider to be beautiful music, art, and architecture have simply been programmed into the universe and by extension into us from birth.

P.S. That charming amigurumi mermaid doll above in the design section was made by Yael. Check out her incredibly well balanced and perfectly proportioned blog: PazzaPazza. It’s wonderful!


  1. Also called the "divine proportion" (by Da Vinci) - when used it is always pleasing for the eye and the ear!
    Lovely post Sheva - a short and poignant explanation of a great matter!

  2. Oh yes and thank you for the hint :-)
    how could I forget?

  3. Wow! What an interesting post. I first heard about the Fibonacci sequence when I read TheDaVinci Code by Dan Brown. Fascinating stuff, great post! xxx

    p.s. I know what you mean about Pazza Pazza, I visit there almost eveery day :)

  4. Sheva,

    You are a super child! YOUR LITTERLY ALBERT EINSTEIN!


  5. Dear Sheva I am Sabri ARIKAN, could you inform me about my golden ratio gauge order please.


    Sabri ARIKAN