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:
- Take any number. We'll use 55 for our example.
- Multiply this number by the Golden Ratio - or phi. This gives us 33.990165 which we'll round off to 34.
- 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.
- Using our example above, let's say the width of a child's afghan is 34 inches. Multiply 34 by Phi (1.62) and you'll see you should make it 55 inches long. If you're working the other direction and the afghan is 55 inches long, multiply 55 by the Golden Ratio (.62), and you'll get a width of 34 inches.
Note: Those with a sharp eye for numbers may have noticed that, not coincidentally, these two numbers are found consecutively in the Fibonacci series.
- A stripe is 19 rows deep. Multiply 19 by .62 to get 12 (11.78) rows. Multiply 19 by 1.62 to get 31 (30.78) rows. Row depths of both 12 and 31 will go well with a row depth of 19.
- You have 25 balls of yarn for your main colour of a multi-coloured article, and fewer than 25 of each of your second and third colours. Multiply 25 by .62 to get 15.5, and then multiply 15.5 by .62 to get 9.61. Using 25 balls of Colour A, 15 and a half of Colour B and almost 9 and two thirds of Colour C will produce a pleasing combination.
- Knitters who love math may want to try their hand at my Moebius Scarf - a loop with a true half twist, and cozy too! With photo.
- Don't forget to check out my other uses of Math for Craft Design.
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