## 14 July 2007

### the Golden Ratio sells pants?

From mathtrek and Gooseania I have learned that a company called The ProportionofBlu is making jeans which they claim are designed based on the golden ratio.

They say, on their (annoyingly flashful) web site:

At the core of every ProportionofBlu creation lies the "Golden Ratio"; a naturally reoccurring sequence of measurements and patterns found in the very building blocks of all life. From the most intricate designs in nature to the most sublime achievements of man, the ratio manifests itself. It lies within the air vortex of a bird's wing, the sensuous curves of a Stradivarius Violin, the structural design of the Great Pyramids and the double helix that houses our very DNA.
It's about form, fit, and functionality. It's about the beauty of everybody and everything. Meticulously hand-crafted, every ProportionofBlu creation is designed "in the ratio" just for you.

The claims about the Golden Ratio being ubiquitous have been debunked (read the Mathtrek post for a start), so it's kind of funny to see the fashion people using it.

The Golden Ratio, by the way, is the positive solution to the equation x2 = x + 1, which is (1 + √5)/2, or about 1.618. It has the property that it's equal to 1 plus its own reciprocal, which I'll use later.

But there are probably some ridiculously large number of measurements that go into making a pair of jeans. It would surprise me more if they managed to avoid having any of these measurements be in a 1.618:1 ratio to each other. This is especially true because jeans come in different sizes, and the measurements that are in this ratio in a size 4 won't be in this ratio in a size 14. (Then again, these people may not even make size 14 jeans, rendering the whole issue moot.) I have a strong suspicion that the golden ratio was not used at all in the design of these jeans, but they figured that by slapping this psuedo-mystical copy into the ads they could raise their prices. And you know what? They're probably right. Lots of smart people work in advertising.

Then again, the golden ratio arises naturally if you look at a five-pointed star, or a regular pentagon. In the diagram at left, taken from the Wikipedia article "Pentagram",
, consider the four lengths indicated by the red, green, blue, and magenta line segments; the ratio between each adjacent pair of these is the golden ratio. The golden ratio also arises in construction of the dodecahedron (which has twelve pentagons as faces) and the icosahedron (which is "dual" to the dodecahedron). Since pentagons have golden ratios embedded in them in this way, you could argue that the United States Department of Defense is built around the golden ratio.