The Law of Margins

Date: 9/2/96 at 19:7:57
From: Miki Nilan
Subject: The Law of Margins

Hi, I understand that you answer math questions, large or small.

I'm an artist who mats her own art for framing.  In a 1928 art book 
("Art in Everyday Life") several pages are given to The Law of Margins 
which is as follows: "In a vertical oblong the bottom margin should be 
the widest, the top next, and the sides narrowest...".  It goes on to 
cite the margins for square and horizontal pieces, and adds: "All 
spaces should be in the Greek proportion.  When the bottom margin is 
decided upon, each side that follows will be about two parts to three 
in relation to the previous space, or in the ratio of about 5:7:11."  

If I choose a 3-inch bottom margin, how do I figure out what the top 
(next widest) and sides (narrowest) should be?  Is it a simple 2/3 so 
that if the bottom is 3 inches, the top should then be 2 inches, and 
the sides l 1/3 inches?  

Is there a prefigured scale for this somewhere?  I apologize for being 
such a nerd with things mathematical, and I thank whoever sets me 
straight.  

I'm curious, too, where I can learn more about this Law of Margins and 
about the Greek proportion.

Thanks so much, Miki

Date: 9/2/96 at 23:54:56
From: Doctor Jodi
Subject: Re: The Law of Margins

Hi Miki!  Thanks for your question.  We're really happy that an artist 
would be interested in writing us about math questions!!
  
The ratio you're talking about is called the Golden Mean.  Here's an 
excerpt about art and the Golden Mean (also called the Golden Ratio).  
You might want to skim the page it comes from, 

 http://pauillac.inria.fr/algo/bsolve/constant/gold/gold.html   . 

A lot of it is equations which you don't need, but the page also 
contains a bit of art related information and a great diagram/picture.

Here's the excerpt:

We start with a problem in aesthetics. Consider the following line 
segment 

                     _________________________________


What is the most "pleasing" division of this line segment into two 
parts? Some people might say at the halfway point: 

                     _________________.________________


Others might say at the one-quarter or three-quarters point. The 
"correct answer" is, however, none of these, and is found in Western 
art from the ancient Greeks onward (art theorists speak of it as the 
principle of "dynamic symmetry"): 

                     _____________________.____________


Here, if the left-hand portion is of length u = 1, then the righthand 
portion is of length v = 0.618... A line segment partitioned as such 
is said to be divided in Golden or Divine section.

excerpt from http://pauillac.inria.fr/algo/bsolve/constant/gold/gold.htmll   
----------------------------------------------------------------------

The Golden Ratio is related to the Fibonacci sequence, the numbers

1, 1, 2, 3, 5, 8, ...

If you notice, each term is the sum of the two previous terms.  For 
example, 2 = 1 + 1 and 8 = 5 + 3.  Nature GROWS in this sequence:  the 
conch-like diagram you saw on the page.

Specifically, the ratio of successive numbers in the Fibonacci 
approaches the Golden Ratio, which is approximately 1.618.  The first 
few ratios are bad approximations:

1/1 = 1
2/1 = 2 
3/2 = 1.5

But starting with 5/3 (1.66), they become fairly good.

--the Golden Ratio 
is a bit more than 1.618.

For more, take a look at the Dr. Math FAQ page on the Golden Ratio and 
the Fibonacci sequence.  It has some very fine diagrams. The FAQ table 
of contents is at

  http://mathforum.org/dr.math/faq/   

Best luck and I hope this helps!

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/