Knitting and the Fibonacci Sequence

Knitting and the Fibonacci Sequence
Nature is filled with patterns, and scientists have long attempted to understand them by using mathematical description. The Fibonacci Sequence is one such explanation of a natural phenomenon known as the Golden Ratio. When numbers are combined to create something, whether it be a rectangle, a shell, or something else, the object appears most aesthetically pleasing when the ratio between the numbers is around 1.618. This ratio, known as the Greek Letter Phi, is very common in nature; a spiraling shell demonstrates this ratio, as does the spacing of petals on a flower, seed pods on a pine cone, and branches on a tree. Knitters can also use this ratio to make stripe widths more pleasing. While converting the mathematics may seem daunting (how does one find numbers that are 1.618 apart?!), a Renaissance mathematician known to us as Leonardo Fibonacci discovered an amazing shortcut.

Fibonacci set up a sequence that started with 1. He added one to one and got two. He added one and two together, and got three. He added two and three together to get five, three and five to get eight, and five to eight to get thirteen. Once can keep going indefinitely. This sequence is a key to the Golden Ratio.

To use the Fibonacci sequence, pick any of the numbers within it starting with three. Then look for the number that immediately precedes it. If you divide the larger number by the smaller number, you will end up with a fraction that comes very close to the value of Phi. For example, five divided by three is 1.66; eight divided by five is 1.6, and thirteen divided by eight is 1.625.

So how can knitters use this information to their advantage? When knitting stripes, don?t make them even. In fact, assign the first color a number according to the Fibonacci sequence, and add colors in stripes that use adjacent Fibonacci numbers. As an example, if one stripe is three rows, make the next color five rows, and the third eight. The pattern will be more aesthetically pleasing than one that?s created with even stripes, because the combined proportions will be closer to the Golden Ratio.

Knitters can toggle between two adjacent Fibonacci numbers, or they can use more. It is usually a good idea to make the darker stripe the smaller number because the deeper shade can overwhelm the lighter one. Want to knit a blue and white striped sweater? Try making the blue stripes five rows and the white stripes eight. Or how about a sweater that?s three different shades of blue? Make the lightest shade five rows, the medium three, and the darkest two. How about a sweater knit with seven gradations of white and black? Make the black strip one row, the charcoal stripe two, the medium gray stripes three, five, and eight, the light gray thirteen, and the white stripe twenty-one!

There is one caveat to the rule of keeping the darker color as the smaller stripe. When using two color with extreme contrast (black or navy with white, for example), personal preference may dictate that the lighter color be used as the smaller stripe. For example, I favor black sweaters with white stripes to white sweaters with black stripes. It is an individual choice here, so hey! You do you!

One is technically the second number of the Fibonacci sequence, but single-row stripes work by themselves. However, this ?exception? is still related to the sequence, as the mechanics of flat knitting require that single-row stripes be knit in multiples of three (to avoid a multitude of ends to weave in.)

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This content was written by Korie Beth Brown, Ph.D.. If you wish to use this content in any manner, you need written permission. Contact Korie Beth Brown, Ph.D. for details.