The Fibonacci Sequence: A Mathematical Striping Pattern

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If you have ever been in a math class, then chances are you’ve heard of the Fibonacci sequence. Sometimes called Fibonacci numbers, the sequence is a series of numbers in which the next number is the sum of the two previous ones. So, 0, 1, 1, 2, 3, 5, 8, 13, and so on.

The sequence has a somewhat twisting history itself. While it’s named for 13^th century Italian mathematician Leonardo of Pisa (he was not called Fibonacci during his life, as far as I can tell), the sequence first appeared centuries before in Indian mathematics. You’ll see this sequence related to the golden ratio in mathematics, and in biological settings, such as the spirals of a seashell or the branching of a tree’s limbs.

The Fibonacci sequence is also, however, a really great striping pattern for knitters.

Fibonacci Sequence Stripes

A Fibonacci striped scarf was one of the first projects I ever knit, and it remains one of my favorite pieces. Using the sequence to create different stripe combinations can create beautiful, simple pieces where the yarn really shines. Plus, if you’re a bit of a nerd (as I am), you’ll get an opportunity to tell people about the Fibonacci sequence whenever they ask about your scarf/cowl/etc.

There are several free Fibonacci-inspired patterns out there, but you can also easily make-up your own. All you need is an understanding of how the sequence progresses, potentially some paper to do some calculations, and some yarn and needles.

Example 1: In and Out

In the swatch below, I decided to use two Fibonacci sequences interlaced with each other. I used some leftover, worsted-weight yarn in brightly contrasting colors. I used the first six numbers (1, 1, 2, 3, 5) to create my stripes. You can see that the blue main color (MC) begins with five rows and decreases to one, while the orange contrasting color (CC) begins with one row and increases to five.

Instructions:

CO 30 sts

(in stockinette stitch)
Row 1-5 with MC
Row 6 with CC
Row 7-9 with MC
Row 10 with CC
Row 11-12 with MC
Row 13-14 with CC
Row 15 with MC
Row 16-18 with CC
Row 19 with MC
Row 20-25 with CC

Example 2: Growing Together

Another possible stripe sequence uses both colors increasing together using the Fibonacci sequence. Each row is added to the previous. For the swatch, I went up to “13” in the sequence, but you can go as high as you like.

Instructions:

CO 30 sts

(in stockinette stitch)
Row 1 with MC
Row 2 with CC
Row 3-4 with MC
Row 5-7 with CC
Row 8-12 with MC
Row 13-20 with CC
Row 21-33 with MC

If you’re not interested in writing all of those rows out, never fear: simply count your rows, refer to the Fibonacci sequence, and you’ll know exactly where you are!

For the number nerd in your life, or even the stripe lover, the Fibonacci sequence provides a wonderful template for the mathematically-inclined. Let me know if you’ve made a Fibonacci piece in the comments and, as always,

Happy Knitting,
Julia

More Resources on the Fibonacci Sequence:

The Fibonacci Sequence

Scientists find clues to the formation of Fibonacci spirals in nature

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