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!

Friday, August 14, 2009

Unrelated geekery...

Hi folks! Haven't posted anything here for far too long -- I really need to get down to finishing off some projects. And taking photos of hats. So, should do some of that soon, but in the meantime I really wanted to post this.
It's a project of local geek Bob, and while it's not technically knitted, it is certainly geeky and extremely awesome:

This was a Triumph

Not much I can say about it other than "wow". So, wow!
And since I'm posting this, I should really put up a link to this too:

Huge success

Awesome, awesome craftiness. Enjoy!