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### The Law of Margins

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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.

Thanks so much, Miki
```

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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:

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

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/
```
Associated Topics:
High School Fibonacci Sequence/Golden Ratio
High School Geometry
High School Practical Geometry
High School Triangles and Other Polygons

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