Monday, August 31, 2009

Prime factors scarf

Right, new project!
This one follows on from the prime number scarf I made a few years ago, which I think was before I started this blog, so it doesn't have an entry here. It was a series of horizontal stripes, with a different colour to represent the primes.
My sister asked me to make a version of this which would give a times-table. I decided the best way to do this would be to pick a colour for each of the primes, and make horizontal stripes made up of the prime factors making up that number. From the prime factorisation you can then work out which numbers divide which, and many more number theoretic properties too.
It's not really viable to do this for *all* the primes, since there are so many, so I had to restrict this to primes under 12, since this is the usual limit for times tables (Is this the same everywhere? Maybe it's just a UK thing?), all other primes are then assigned one colour. So it's a kind of colour-coded version of Eratosthanes's sieve.

I think it might have been a better choice to say that not just primes over 12, but any number with a prime factor over 12, should be left blank, since this won't appear in the times-table at all. This would give a rather different effect - the first way means the colours get more broken up as the scarf progresses, as the larger numbers tend to have more distinct prime factors, so they colours are all mixed together. The latter way would be less cluttered, with the "prime over 12" colour coming to dominate quite strongly be the end.
Knitting-wise, this scarf involves rather a lot of stranded knitting, so I've been trying out the trick of holding yarn in each hand, which has been quite fun. The hardest part is that the number of strands varies, from just one up to three, so keeping the tension even is quite a challenge.

I should mention too, that I've just come across this counting pane design by the Wooly Thoughts folks, which seems to work along quite similar lines, although the factors they colour are not restricted to primes. Go look! Also check out their other things, they have *loads* of cool mathsy knitting projects!

Happy knitting everyone!
Hugh.

3 comments:

Ahava Jora said...

Ah, interesting. I'd love to see a pic of this scarf!

Jhadur said...

I'm hoping to get through it quite quickly, so I'll take pictures when it's done. It's quite ... loud, I went for some pretty bright colours and they contrast a lot. I am wondering about making a more subdued version afterwards though, possibly with shades of blue and purple. I suspect the effect will be pretty dramatically different that way.

mathcathy said...

When my Dad learnt times tables, they were taught up to 16.