Fibonacci Striped Scarf

Fibonacci was an Italian, one who came up with a particular kind of mathematical sequence. A Fibonacci sequence starts with two numbers. The third number is the sum of those two numbers. The fourth number is the sum of the previous two numbers. Repeat forever to build a sequence. The Fibonacci sequence that you’re most likely to come across is this one:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.

Why am I telling you this? Because playing with Fibonacci sequences – and making Fibonacci stripes – is knitting for your inner math geek. As you might have expected, my inner math geek wanted to play.

If you knit an increasing Fibonacci sequence in one colour – like red – and intersperse it with a decreasing Fibonacci sequence in a second colour – like black – then do the mirror image of that, you get a scarf like this:

fibonacci.JPG

This is Mr. C.’s new Fibonacci scarf. This is easy knitting.

You can knit this scarf either in the round on a circular or DPN’s or you can knit it flat and seam the long edge later. Don’t cut the yarn after each stripe – who needs to have all those ends to sew in? – just carry it up the side or the inside to the point where you need it next. It’ll stay cozy inside the scarf when you’re done and no one will know.

Here’s the sneaky bit – a lot of the numbers in the sequence are odd numbers, whic doesn’t matter if you knit in the round. Just pull the colour you need up the center. If you’re knitting it flat, though, this might confuse you. You’ll knit one row of red, for example, need the black to purl back but it’ll be at the wrong side of the work. which means you’ll knit one row, then need the other colour and the end of that colour will be at the other side. If you knit back and forth on circular needles instead of using straights, you can just knit your next row with the black. Just push the work to the other end of the needle. Trust me, it works – and you’ll feel so sneaky when you do it!

For this scarf, I used one ball of Patons Classic Merino in red and two in black tweed. The red is really tight, so if you plan to cut the ends despite what I’ve said, or if you want red in the fringe, you’ll need a second ball. This scarf finished at 7″ wide and 58″ long without the fringe.

You’ll need 4.5mm needles and a crochet hook. My gauge on this scarf was 4 sts to the inch and 6 rows to the inch – gauge isn’t critical on this project, so long as you like the fabric you’re getting BUT if you knit looser, you’ll need more yardage to finish.

Colour A is black and colour B is red.

Cast on 60 stitches in colour A. If working in round, join into a round. Knit rows as follows:
A 34 rows
B 1 row
A 21 rows
B 1 row
A 13 rows
B 2 rows
A 8 rows
B 3 rows
A 5 rows
B 5 rows
A 3 rows
B 8 rows
A 2 rows
B 13 rows
A 1 row
B 21 rows
A 1 row
B 34 rows
A 1 row
B 21 rows
A 1 row
B 13 rows
A 2 rows
B 8 rows
A 3 rows
B 5 rows
A 5 rows
B 3 rows
A 8 rows
B 2 rows
A 13 rows
B 1 row
A 21 rows
B 1 row
A 34 rows

Cast off. If you knit flat, use mattress stitch to seam the long edge. Lay the scarf flat, right side out, with either the seam or the ziggy line where you joined the work in the round at one fold. Take a crochet hook and a length of colour A to work a line of single crochet across each end closing the end of the tube – each stitch of crochet will go into a stitch on the top layer of the scarf and the corresponding one on the bottom layer.

Repeat on the other end.

For fringe, cut 12″ lengths of colour A. Take three and fold them in half, then use the crochet hook to loop them through the end of the scarf and knot. I put a clump of fringe like this on every second stitch.

Ta da! There you go – you can head out in the fall chill, revealing your inner math geek to knitters everywhere.

35 thoughts on “Fibonacci Striped Scarf

  1. I don’t have an inner math geek so it took me awhile to deconstruct your sequence. (And I had to have an extra dose of caffiene and reread the directions twice.)

    I like the symmetry.

  2. I love how that turns out and am not going to lie… I kind of am a math/science geek… I looked at the pattern and thought, “Oh, that makes perfect sense.” >.

  3. I want to knit this in round but and I was wondering what length my circular needles should be…mine are 29″ and that seems really long…any thoughts??

  4. Thanks Gabriel!

    DizzyGirl, I think I’d use 16″ circulars, or even a set of 8″ dpns. My finished scarf is about 7″ flat, so that’s 14″ in the round. With 24″ or 29″, it would be stretched out too much.

    Come back and give me a link when you’ve finished. I’d like to see another one!

  5. Late to the party, but . . . OMG, thanks so much for the tip about using the other end of the circular to knit in the second color. So simple, but so awesome.

  6. This scarf is so awesome! I will try knitting with circular needles just to accomplish this scarf. However, I don’t understand what to do after I’m done knitting, as in how to clean up the yarn that shows from switching colors? Or I don’t have to do anything because I’m knitting with circular needles?

    Please advice because I’m VERY new to knitting (just started!)

  7. You won’t have to do anything, Tanya. You will have carried the yarn up the inside of the tube when you change colours, so there won’t be any ends to weave in. And the stretches of yarn from one colour block to the next will be inside the tube – only you will know they’re there.

    Knitting this in the round is easy peasy. Go for it!

  8. ok i think i figured it out!
    did you use stockinette stitch for this?
    thanks for answering my questions….i really just started knitting!

  9. Hi Tania –

    Yes, it’s in stockinette, so if you make it in the round (on circular needles), you’ll just knit and knit and knit.
    :-)

  10. sorry i have another question =(

    what does “If working in round, join into a round” mean?

    if its round….its a cylinder tube, and not a flat scarf? i’m so confused.

    • Tania – Just that you cast on flat. If you intend to work in the round from that point onward, you need to join the cast on stitches into a circle. You can do that by pulling them around the circular needle until they cover it, then knitting into the first cast on stitch. That will make the work into a loop.

      Just try it. It takes longer to explain than to just do it!

  11. hmmm i understand making something round, like for a gloves or a hat…but a scarf is flat…no?
    why would a scarf be joined into a round? i’m confused.
    i just bought my circular needles for this project today =)

  12. After reading your post many many times, I am assuming your scarf is like a long tube, thus when flattened out, it has 2 layers. Is this correct?
    Then you seal the top and the bottom of the scarf…right?
    I really thought you were knitting flat with circular needles…..

    • Yes, Tania, the scarf is a long tube that is flattened.

      You can knit it as a tube, then close the ends. Or, you can knit it flat (on circular needles, which is what I did), then seam it on the long side when you’re done, then close the ends.
      :-)

  13. Hi, I did a google search for Fibonacci Scarf knit and found your site. Thanks for posting it. It is a beautiful scarf and definately one I’ll be making soon.

    • Hi Joel –

      It’s a quick and easy knit. I hope you like it. My husband wears his all the time.

      It’s on Ravelry as a pattern, too. There you can see the other versions of it.

  14. Hi there, I found your Fibonacci scarf pattern here earlier in the year. Nine weeks later, I’ve finally finished it (pale pink and charcoal striped version)! I like longer scarves, so I knit mine as two full pattern repeats, so it has come out quite long (possibly a bit longer than I really expected….) – very cool. Now for some matching mittens…need to hurry up on those as winter is setting in quickly down here in NZ.

  15. I want to make a stripped vest for my husband. It is all one piece until i get to the armholes. I have a cream and brown colored yarn that I want to stripe together. I understand the fibonacci math but can’t seem to put it into practice. Do you have a recommendation for a stripping sequence for this vest. Thank you.

  16. I arrived here from a link in a fanfiction and I am glad.
    I have already saved the pattern to make a fibonacci scarf.
    I am think to make it with my knitting mill.

    • Have fun with it, Jessica! My husband wears this scarf all the time. (I think he likes telling people about Fibonacci.)

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