Golden ratio

Cut a line so that the whole is to the longer part as the longer part is to the shorter, and the ratio you get is roughly 1 to 1.618. It is written with the Greek letter phi, it is irrational, and it is the positive solution to the equation that says a number is one more than its own reciprocal. The property that makes it interesting to a designer is what falls out of that: take a rectangle of that ratio, cut a square off one end, and what is left is another rectangle of exactly the same ratio. The shape contains a smaller copy of itself, forever, which is why a layout divided this way can be divided again the same way and still look related to itself.

The usual claims about it deserve to be met with more scepticism than they get. The idea that people find the proportion inherently beautiful traces to a set of nineteenth century preference experiments that have replicated poorly ever since, and the famous sightings in the Parthenon, in the nautilus shell and in Renaissance painting are mostly measurements chosen after the fact, from a range wide enough that some ratio near 1.6 was always going to appear. The honest summary is that there is very little evidence the number does anything special to a viewer.

What survives that is still worth having. The value of any ratio in layout is that it is a rule: pick one and the widths, the gaps and the sizes in a design come out of the same arithmetic instead of being negotiated one at a time, and the result reads as deliberate because it is. The golden ratio is a decent pick for the job, and its self-similarity is a real advantage over the alternatives, since a golden split can be split again without introducing a new number. The rule of thirds is the cheaper rule that does most of the same work, and a modular scale is the same idea applied to type sizes, where a constant ratio between steps is what keeps a heading and its body text feeling like a pair.

In practice treat it as a starting number, not a verdict. Derive the split, then round it to whatever spacing scale or column grid the rest of the system runs on, because a proportion that lands on 172.4 pixels is worse than one that lands on 176 and agrees with everything around it. Then look at the result: optical adjustment outranks the arithmetic every time, and a proportion that measures correctly but reads as top heavy is simply wrong. The ratio is a way to stop arguing about numbers, which is a genuinely useful thing for it to be, and it is not a proof that the numbers are right.