The Golden Rectangle

I remember learning about the Golden Rectangle in Geometry class, back in high school. "Aha!" I thought, "there is something behind my obsession with this 3x5 shape!"

The golden rectangle is based on the "golden ratio," defined in Wikipedia as:

... a mathematical constant, usually denoted by the Greek letter (phi). The figure of a golden section illustrates the geometric relationship that defines this constant. Expressed algebraically:

This equation has as its unique positive solution the algebraic irrational number

Wikipedia also shows how to construct a golden rectangle-- remember doing this in school, with a ruler and a protractor?

Construction of a golden rectangle:
1. Construct a unit square (red).
2. Draw a line from the midpoint of one side to an opposite corner.
3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle.

A 3 by 5 rectangle is not exactly a golden rectangle, but it's very close: the ratio is about 1.6666..., a difference of only about 3%. The dimensions of a pocket Moleskine notebook are approximately 3.5 x5.5 inches, which is a ratio of about 1.57142...., which is a difference of only about 2.8% from the golden ratio. Perhaps this is why the Moleskine-sized notebook has become so popular lately, as opposed to the 3x5" or 4x6" notebook formats that used to be more common. (4x6 is only a ratio of 1.5, even further away from the golden ratio!)
It will be interesting to see which of my favorite notebooks and objects come closest to the exact proportions of a golden rectangle.