Proportion and Scale

​A designer friend of mine recently asked if I had any reference material to help her determine the proper proportion and scale for pillows on a sectional sofa for a client.  “Well, yes,” I replied, “I did an article for a window coverings trade magazine a little while ago that addressed proportion and scale, and what a “pleasing proportion” is all about.”  For definition purposes, scale is the size of something in relation or comparison to other things, and proportion is the relationship of the part or parts of something to the whole).
 
So, here’s a little tidbit from that article to give you a small taste of proportion.  Spoiler alert…there is math up ahead…but it’s algebra, and you can handle it… 

It all started with those genius Greeks

Way back when the Greeks were building their masterpieces of sculpture and architecture like the Parthenon, they developed some “pleasing proportions” and a concept called the “Golden Section” or “Golden Mean.” From a geometric model, they developed a progression of numbers ― 1, 2, 3, 5, 8, 13, 21, 34 ― in which the two preceding numbers added to each other develop the next number in the progression. Thus, 1+2 makes 3, 2+3 makes 5, and so on. And this sequence forms the basis of proportions we’re all familiar with (think photo processing: 3x5, 5x8, 8x13, 13x21, etc.). They further developed the Golden Rectangle, also known as the Golden Mean, Golden Ratio and Divine Proportion. It’s a ratio or proportion defined by the number Phi (=1.618).
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Now that we know about Phi, our magic number, how do designers apply this to concept?   Well, phi is everywhere--science, nature, human form, architecture, art, and everything beautiful, including your interiors!   In the photo from Antiquefireplace.net, we see the graphic depiction of the golden mean ratio (looks like a nautilus) overlaid on a classic door opening.  Such beautiful architecture, love that classic look and the floors.  When we’re not designing the Parthenon, we can use the proportion of .618 when we are determining where to place something, and symmetric, right smack dab at the center, isn’t right.  Think chair rail height.  Think size of rectangular pillows. Think architecture of doorways and windows.  Think placing your drapery pole either .618 of the space down from the ceiling, or up from the window (never exactly in between!)  The Golden Mean applies to anything, vertically or horizontally…a 3x5-foot table or art piece is in a pleasing proportion, as are multiples of these dimensions (a room 12x20 feet or 15x25 feet). 

The Golden Standard

The Golden Mean/Golden Ratio/Divine Proportion can be derived with a number of geometric constructions, each of which divides a line segment at the unique point where:

Phi = (a + b) / a = a / b = 1.618
If you take a line as 1, then a =.618, and b = .382

This division of a line at 0.618 makes a pleasing proportion versus an exact division of the line. Now, going back to our pleasing proportions of 3/5, 5/8, 8/13, etc, you will see these ratios are always very close to the Golden Mean of 0.618.

Summing Up

​Thanks for getting through my Math rant.  Can you tell I was a Math major for my undergraduate degree and geometry was pretty important in my mental marriage of math and design?
 
All you need to remember is .618.   Trust me.