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Fibonacci or Golden Rectangle shawl

Fibonacci (fee-bo-natch-ee) was a 13th-century mathematician who developed a sequence of numbers based on the Golden Rectangle.  For a great explanation of the Golden Rectangle, watch “Donald Duck in Mathmagic Land.”

Each number is the sum of the previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21, and so on. In order to knit with stripes that are of different widths but still evenly distributed, many use the Fibonacci sequence. It gives rhythm and movement rather than a chunky look to items, especially those that use odds and ends, scrap, or novelty yarn.

You may use this sequence in any knit garment, but I used them when I was making prayer shawls.  I got bored with the standard pattern and just one yarn.  Then I stumbled across “The Yarn Stash Workbook” by Laura Militzer Bryant.  I was fascinated by the cover and bought the book on the spot.

When I used the Fibonacci sequence, as the book suggests, in order to use up odds and ends and avoid a chunky stripe, I created some really unique and interesting shawls.

Before I share the pattern, here are a few things I learned along the way:

  • Stick with one color family. The closer in hue, the better.  The beauty of these shawls is the subtlety of the variation, IMHO.  If you use a multicolored novelty yarn in a single-color shawl, all of the other colors will pop, and the base hue will blend in.
  • Use novelty yarns wisely and sparingly.  I love glitter and novelty yarns, and they are fun to work with.  But take it easy.  Using silver as well as gold, too much fun fur or ribbon, etc. can look tacky.  Less is more here.
  • Use wonderfully soft yarn, especially if this is a shawl or other garment.  Novelty yarns especially can be scratchy or prickly; not fun to wear.

This is a really easy shawl to make, as it is just garter stitch – all rows are plain knitting.  I use size 13 circular needles with at least a 24” cable.

You will need at least three different yarns: A, B, and C.  I like Lion’s Brand Homespun and Pound of Love for A and B.  C is one or more novelty yarns.  There should be an odd number of novelty yarns (1, 3, or 5).  If you have more yarns that you want to use, put them in three or five piles and count each pile as one yarn.

Cast on 125 stitches with Yarn A and, leaving about an 8” tail, cut the yarn.

Tie Yarn B to Yarn A at the needles, leaving another 8” tail. In other words, every time you switch yarns, you leave and add a tail, which turns into a self-fringe. I love not having to add fringe and that this fringe exactly matches the rows of the shawl! Use a square knot and snug it up tight to the needles. I actually use my hand span to measure the fringing quickly, and you can trim and even it out later.

Knit the first row in Yarn B.

Knit the next two rows in Yarn C.

Knit the next three rows in Yarn A.  So now, counting the cast-on row, you’ve got: A, B, C, C, A, A, A.

Now knit another sequence, starting with Yarn B: B, C, A, A, B, B, B.  If you are using more than one Yarn C, switch yarns or piles with every sequence.

Now knit the third sequence, starting with Yarn C: C, A, B, B, C, C, C.  These three sequences make up one section of 21 rows.

Knit four more sections, binding off loosely on the last row.

For a scarf just do one or two sections, making it as long or short as you like, casting on between 100- 200 stitches. For a larger shawl cast on 150 stitches and knit seven sections.

This sequence may be used on all kinds of knitted items: pillows, throws, even garments. I made a Fibonacci Ruana for a friend and it turned out pretty well.  Have fun!