(Insert Ja’mie voice here): “Um, so anyway, I have the best news…”

… I just got back from Stitch ‘n’ Bitch, and have made some major progress on a mathematical knitting problem I’ve been grappling with. Here’s the story: just over a year ago, I wanted to knit an armadillo that you could roll up into a ball. Kind of like a popple, but I actually wanted a perfect sphere, not just a teddy with a pouch that you pull over its head. So I started thinking about how you would go about knitting a short-row sphere, i.e. one you could knit that had a resulting split across half the circumference allowing you to place folds in it to create a hemisphere (kind of like a foldable hood on a baby’s carriage, or an awning). I found the problem mathematically a little daunting, and so quickly stopped thinking about it (I ended up knitting these dice). Until recently…

At the SnB I’ve made friends with Jennifer and Lisa, two atmospheric scientists from the Dutch meteorological institute. Needless to say, they’re both better than me at maths, and after some brainstorming with Jennifer and her husband last week, tonight I placed the problem before Lisa and – you guessed it – we have a formula! Here’s what we came up with:

Basically, what I needed to know was: for each cast-on stitch on the needle, how many rows are needed above and below it to produce a circle of latitude of the right circumference for that position on the sphere’s surface? So using trigonometry (plus some white wine and a shot of strong Dutch gin) we figured out a way of calculating each circle of latitude as a function of the position of each stitch on the needle. Then you can figure out the short-row pattern, and knit the sphere in one piece. Phew and yippee at the same time!

Now I just need to get Jennifer to put the formula into an excel sheet for me, and then I’ll have a generator that will calculate the pattern for any number of cast-on stitches.

(Insert evil laugh voice here): Mwuh-ha-ha-ha-ha-ha!

Quote of the day:

A man remarks, in anger torn,
“No rose exists without a thorn.”
Yet think of how his anger grows
At all the thorns without a rose!
– Eugen Roth


3 Responses to “Eureka!”

  1. 1 Serena
    2 April, 2008 at 8:13 am

    Wow.. this looks complicated indeed! I am looking forward to follow your knitting of this project.

  2. 2 Ginger
    3 April, 2008 at 10:29 am

    *gulp* sounds complex! Now you got us all interested. We’ll be sure to watch for updates on this project đŸ™‚

  3. 3 walkaboutknitter
    5 April, 2008 at 7:29 pm

    Hi Brent, walkaboutknitter aka heather, responding to your comment on my blog. Although I love maths, I suspect that you’re over thinking your sphere.

    These patterns from the early days of the venerable knit list uses short rows to form segments (a bit like the segments of citrus fruit) to form a side to side knitted ball. based on what you’ve outlined, you could easily adapt this to be an attached bit that your armadillo could be rolled up into.

    Judy Gibson also came up with a swirl version.

    I’ve used and adapted the basics surrounding these items very successfully over the years.

    I hope you’ve followed the links to my Positively Polygonal pages.

    Oh, and BTW, one of my current projects is to knit a base ball (a specific sphere) based on the info at wolfram maths

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