Rabbits, Math, Crochet Color Striping, and the Fibonacci Sequence

Leonardo Pisano Bigollo, a medieval Italian mathematician better known by his nickname Fibonacci, is best known for coming up with the answer to the simple question, “How many rabbits would you have in a year if you started with a pair?” He posed this question in his book Liber Abaci, originally published in 1202. His surprisingly simple answer led to the solution that has become known as the Fibonacci sequence.

The Fibonacci sequence is a series of recursive numbers (the first known in Europe) where the next number is determined by adding together the two previous numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so forth. Fibonacci numbers are frequently found in nature in everything from leaves and flower petals to seashells and honeybee family trees.

fibonacci sequence

Use the Fibonacci Sequence to Calculate Color Striping

In the Parallel Celebrations Shawl from Love of Crochet Winter 2017, I used the Fibonacci sequence to determine the width of each stripe as two colors cross each other. The shawl begins with the largest number (55) and works down the sequence in one color as it works up the sequence in the other color, like so: 55, 1, 34, 1, 21, 2, 13, 3, 8, 5, 5, 8, 3, 13, 2, 21, 1, 34, 1, 55 (Figure 1).

fibonacci sequence

Variations with the Fibonacci Sequence

You can use these numbers in many different ways to create unique and pleasing striping patterns. Here are a couple of ideas: Choose three colors and use them successively in a longer striping sequence; for example, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8 (Figure 2). By using fewer colors than there are stripes in your sequence, each repeat will begin with a different color, which results in delightfully balanced random-looking stripes.

You could also use the smaller numbers of the sequence seen in the Parallel Celebrations Shawl with three colors multiple times: 5, 1, 3, 2, 2, 3, 1, 5, 1, 3, 2, 2, 3, 1, 5, 1, 3, 2, 2, 3, 1, 5, 1, 3, 2, 2, 3, 1, 5, 1, 3, 2, 2, 3, 1, 5, 1, 3, 2, 2, 3, 1, 5 (Figure 3).

fibonacci sequence
As you can see, there are several ways to apply the Fibonacci sequence to your crocheting that can give you vastly different results. You may be thinking of shawls or afghans when you think about stripes, but this sequence can be used on virtually any project. Give it a try on amigurumi, table settings, sweaters, bags, and more.

Connie Lee Lynch is an Army wife, a new mom, and a part-time crochet instructor. She loves that each piece of crochet she designs feels like magic as it is transformed from an idea into a unique handmade piece of art. This piece was originally published in Love of Crochet Winter 2018.

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