Fibonacci beanie (in three colours)

The Fibonacci sequence is the basis for the golden ratio – a pattern of numbers that occurs naturally in nature and is aesthetically pleasing to the eye. This beanie uses the sequence three times, in a recursion, as colours 2 and 3 are summed together in colour one, all while still in sequence.

I wanted to knit a beanie that wasn’t bulky, was long enough to be snug around the ears, and simple enough to let the wool and pattern do the talking. I will revise the pattern slightly to give an alternative shaping of the crown, but that will happen in the future. This one looks good and works very well.


You will need 3x50g balls of 5ply (I used Patons Bluebell 5ply in Navy, Beige and baby Blue) – (C1, 2, 3). You will use more of C1, and less of C3. If you are just using the beanie pattern, you will need 2x50g balls of 5ply.

2.5mm circs
2.5mm dpns
16 markers

*note this was made for an adult male head (roughly 22″) and has a length of 8″ from edge to crown.

Cable c/on 153 stitches.
Join, K2 P1 to end of row. Repeat for 15 rows.
16th row K16 inc 1 = 162 stitches
Knit 92 rows (see full pattern below)
93rd row – K54 K2tog K53 K2tog = 160 stitches
94th row knit, placing stitch markers after every 10 stitches (16 groups of 10)
95th row K7 K2tog K1 – repeat rest of row.
Repeat pattern knitting to last three stitches, K2tog, K1 until 16 stitches left, moving to dpns when too small for circs.
Next row K2tog – repeat = 8 stitches.
Thread wool through stitches, pull tight, and weave through to finish.

Colour 1 – 21 rows K3 P1 for 15 rows, K9 inc 1 (16th) K rest
Colour 2 – 13 rows
Colour 3 – 8 rows
Colour 1 – 13 rows
Colour 2 – 8 rows
Colour 3 – 5 rows
Colour 1 – 8 rows
Colour 2 – 5 rows
Colour 3 – 3 rows
Colour 1 – 5 rows
Colour 2 – 3 rows
Colour 3 – 2 rows* begin decreases
Colour 1 – 3 rows begin Kx K2tog K1 rows
Colour 2 – 2 rows
Colour 3 – 1 row
Colour 1 – 2 rows
Colour 2 – 1 row
Colour 1 – 1 row K2togs, c/off

A photo of the beanie on the intended head size follows. I will post the pattern for the double rib Fibonacci beanie (which starts with the smallest number first), and measures 7.25″ from edge to crown when it returns from the UK this weekend. It too is knitted on 2.5mm needles with 5ply wool.

I used row numbers and not measurement for those who just want to use the beanie pattern and do their own thing with stripes, or plain or patterns. Enjoy!

Feel free to post if you think this pattern needs more clarification.



This is pattern is free for personal, non-commercial use. Further use requires permission from the designer (me).

Fibonacci sequencing devised by Christopher Monteith



  1. oh hooray! thank you CF! I’m not going to make it yet but it’s going on the file. I’ve been waiting. Ta muchly!

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