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/
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