COMM 207: "Golden ratio" and page layout

It's a long way from copyediting and page makeup to the ancient Greek mathematician/philosopher Pythagoras -- about 2,000 years, to be exact -- but one of the principles goes back to the ancient Greeks. It's a proportion sometimes known as the "golden ratio" and still followed (usually by intuition).

Basically the golden ratio is the ratio between the sides of the Parthenon or, for that matter, the human face. There are pictures, diagrams and -- for those whose minds are capable of understanding them -- mathematical equations in the basic Wikipedia article on the concept.

Explains Bruno Maddox, in a June 1 article on classical proportions in plastic surgery (!) in Discover magazine:

... The ancient Greeks, for their part, were convinced that an explanation of, and definition for, Beauty was as concrete and discoverable as the answer to why the days got shorter in winter or why your toga weighed more after you’d gone swimming in it. Indeed, no less a thinker than Pythagoras, he of hypotenuse fame, logged some impressive early results. In music, Pythagoras showed that the notes of the musical scale were not arbitrary but reflected the tones produced by a lute string—or any string—when its length was subdivided precisely into such simple ratios as 2:1 or 3:2. In architecture and design, similarly, he managed to show that the shapes people found most pleasing were those whose sides were related by the so-called golden ratio.

The golden ratio, briefly, is the proportional relationship between two lines a and b such that (a + b) is to a as a is to b; in other words, the ratio between the whole and one of its parts is the same as the ratio between its two parts. This doesn’t sound like much in algebra form (a/b = (a + b)/a) and still less when expressed as a decimal (1:1.61814). But draw a rectangle—or build a Parthenon—with sides of a and b, and the sheer cosmic rightness of the thing leaps out at you. If you were to be stranded on a desert island with one particular rectangle, that’s the one you’d go with. Palpably, it’s the first rectangle that occurred to God when he realized he needed another four-sided, right-angled shape to complement his juvenile masterpiece, the square.

This was good enough for Plato, the 800-pound gorilla of ancient Greek intellectual life, to include Beauty as one of his famous forms: those transcendent, invisible archetypes of which this reality is nothing but a set of blurry ramshackle imitations. Beauty was not in the eye of the beholder. On the contrary, to borrow Plato’s legendary cave metaphor, the beholder had his back to Beauty, able to see only its flickering shadows on the grimy cave wall of reality.

In short, the Science of Beauty was inaugurated by the two classical thinkers upon whose shoulders the science of pretty much everything else would eventually come to rest. Among historians of science, that’s what is known as a rollicking and auspicious start.

Maddox is suspicious of any claims to precision in the theory, which was explained to him in great detail and with breathtaking precision by a Southern California plastic surgeon, but he thinks there's something to it ... especially if you stick to ballpark figures.

So, after laying out too many newspaper and newsletter pages to count over the years, do I.

If you're interested in learning more, see also Wikipedia's article Canons of Page Consruction. And if you're really interested, scroll down to the links at the bottom of the page to terms used in typography. Follow those links, and you'll find the difference between a "widow" and an "orphan."