Posts Tagged ‘mathematics

22
Apr
08

Dodecahedron (and snub is back)

Hi y’all. Last week at work I made a dodecahedron out of my magnetic sticks and ball-bearings. Here it is:

Actually, only the blue sticks form a dodecahedron. I had to use all the red, green and yellow ones to stabilise it since it’s made of pentagons, and pentagons aren’t naturally very stable. The thing kept collapsing.

And yes, that’s a snub disphenoid in the background.

Random quote:

Me: “Where are all the good-looking guys?”
M.: “Grooming.”
In the pub last Saturday night

11
Apr
08

Perfect sphere

I had a very productive day today. I hung up the new curtains that anita had made for me:

And I knitted a perfect sphere:

And now I’m off to Natasja’s for dinner. She wanted to cook for me, since it’s such nice weather. Go spring!

Random quote:

Conductors must give unmistakable and suggestive signals to the orchestra – not choreography to the audience.
– George Szell

09
Apr
08

Snub Disphenoid

Yesterday at work I made a snub disphenoid out of ball-bearings and magnetic sticks. Here it is:
The snub disphenoid is one of the 92 Johnson solids, which is a group of polyhedra whose faces are all regular polygons (equilateral triangles, squares, pentagons, hexagons etc.), but that aren’t Platonic or Archimedean solids, prisms or antiprisms. Most of them are constructed by “cutting and pasting” bits of other more regular polyhedra together, but not this guy. He’s an elementary Johnson solid. He’s an individual. You can’t fool him.

I think he’s cool.

Random quote of the day:

“I love my job, I love my job, I love my job…”
Emily, from The Devil Wears Prada

01
Apr
08

Eureka!

(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