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The Golden Ratio

by Linda

This is one of the math concepts I use when designing a new pattern. In fact, it's probably the one of the three I use most often. For an overview, please see Math for Craft Design.

Below is a bit of information about the Golden Ratio and a few examples of how to put it to use. You may want to read a bit about Fibonacci numbers first if you're not familiar with them.

The Ratio

The Golden Ratio is also called phi - with a lowercase p. Okay, technically it's a decimal, but at any rate, it's generally accepted to be the number

0.618033 (rounded off to six decimal places).

I normally round up to 62 percent or .62 when I use it.

Why This Number is Special

I'm sure there are at least a half dozen other routes to the Golden Ratio, but this is my understanding of the most simple way. When a particular Fibonacci number is divided by the next in the series, the result comes very close to the Golden Ratio. The higher you are in the series of Fibonacci numbers, the closer you get.

A Related Number

A number very closely connected to the Golden Ratio is Phi - with an uppercase P. It's generally accepted to be the number

1.618033 (rounded off to six decimal places).

I normally round up to 162 percent or 1.62 when using it.

How phi and Phi are Connected

They're the only numbers that work as follows:

  1. Take any number. We'll use 55 for our example.
  2. Multiply this number by the Golden Ratio - or phi. This gives us 33.990165 which we'll round off to 34.
  3. Now we'll start from the other end with 34, and multiply it by Phi. This gives us 55.013122 which we'll round off to 55. Right back to the original number.

Okay, this may not seem like a big deal until you realize that Phi is simply the Golden Ratio - phi - with 1 added to it. Try that trick with any other number. :)

Practical Uses

All you have to remember to use the Golden Ratio is .62 and 1.62 - or 62 percent and 162 percent - and you're all set. Multiply your number by .62 or 1.62 to get a smaller or larger number that will go well with it.

This is especially handy when the Fibonacci or Lucas numbers don't quite fit your needs.

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