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:

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, which 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.