Fibonacci Scarf and Prime Factorization Hat

What do you knit for a mathematician that is aesthetically pleasing and also intellectually interesting? Voila! For Ari's birthday I made him a Fibonacci Scarf and a Prime Factorization Hat. I gave it to him and told him that he had to find the math in each gift, and he was so excited and impressed when he figured it out!

The idea of the Fibbonaci scarf is simple: stripes according the the Fibbonaci sequence, which is a famous mathematical sequence found by adding the two previous terms to get the next term. 

ie. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. This scarf is really four short sequences, each half contains an increasing and a decreasing sequence overlapped with each other. 

The only math-y part of the prime factorization hat is the band around the bottom. I got the idea from this amazing prime factorization sweater pattern. The prime factorization of a number is simply any number broken down into it's prime factors. For example: the prime factorization of 16 is 2x2x2x2, and the prime factorization of 15 is 3x5. The band starts at one (the grey square, since one is special and isn't really prime) and goes around. Each new prime gets it's own color, and each composite (not prime) number is represented by it's prime factors. So clever. It only took him a few minutes to figure it out though.

Yarn Scrap Gift Bags

A great way to use up yarn scraps is to make little gift bags, and fill them with chocolate! The recipient gets to eat chocolate and have cute little bags to put keepsakes in later. I filled these with chocolate covered almonds and gave them to my roommates for the holidays. Aren't they adorable?

Ear Flap Hats

I've been really into knitting people earflap hats lately. They are quick, fun, and have a lot of room for creativity and personalization! This is the one I made for my sister this Christmas.

See also Ari's math hat!

Fair-Isle Knitting Experiments

I stumbled upon this book in a yarn shop in Port Townsend the other day, and I just had to have it. I've always enjoyed color work, but I have the feeling that there are some tips and tricks to it that I'm missing. Not anymore!

My current project is to fine tune my fair-isle techniques, and this hat was my first experiment. Fair-isle knitting just means knitting intricate patterns that involve stranding, meaning that you carry the yarn short distances on the back of the knitting. Little did I know there are ways of doing color-work without stranding. I can't wait to learn about that, it's called intarsia. Stay tuned!