New Pattern!

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Because You Can Never Have Too Much PI – pi fez!

Okay, it’s a beanie – unless you felt it into shape. And add a tassel. The numbers down the sides list π to 50 decimal places. To  be specific, it starts: Π ≈ 3.14… i.e., π approximates to 3.14, etc. Cos that’s how I roll.

Fun Facts About Π:

  1. 50dp is overkill. Only 39 decimal places of Π are required to calculate anything to redundant levels of precision – for example, you could navigate across the known universe and be no more than one atom’s width from your intended destination at the end. More than my satnav can manage…
  2. The Guinness World Record for memorising Π is held by Lu Chao – 67,890 digits. Some people really have nothing better to do.
  3. Π is known to 10 trillion dp – calculated by Shigero Kondo in October 2011, using an ordinary home computer. Mr Kondo was unavailable to comment at his parents’ basement, as he was waiting for a pizza delivery.

What is this thing called Mathematics?

There is an apocryphal tale of the French mathematicians who published collectively under the name Nicolas Bourbaki, who apparently wrote 200 pages on the number one alone (Bergamini, 1972). I cannot say I believe this story completely, having heard similar anecdotes of topics broad (psychology) and narrow (the modern Italian historical novel). The experts shake their heads and chuckle wryly at the naivety of asking for a definition. Thus forewarned, I shall not fall into this trap: I shall say only what mathematics means to me. Mathematics is, to me, the science of number; its uses, both practical and theoretical (Courant, Robbins & Stewart, 1996); and associated notations. I will explain my take on these in reverse order. Notations I do not regard as especially important: Shakespeare is still Shakespeare, whether in the original Elizabethan English, translated into Norwegian, or performed in British Sign Language. It is unfortunate that notation is often the first thing people think of on hearing the word ‘mathematics’. Perhaps more effort is needed in schools to describe this as a code, shorthand, or language.

The uses of mathematics I regard as practical, meaning applied or descriptive, or theoretical. The practical element is relatively easy to explain: a shepherd counts his sheep to keep track of them, plan grazing, and so on; that number is also a handy descriptor for others, rather than taking them to the hills to see for themselves! This practical element also elucidate processes and phenomena which cannot be observed or comprehended directly, such as the detection of orientation in vision (Anderson, 2001) or the origin of the universe. The phrase ‘theoretical uses’ is something of an oxymoron – perhaps another synonym of ‘use’ would be better here – service, practice, exercise… However, I am inclined to think that theory – the study of a subject purely for the subject’s sake, as it were – is a ‘use’ whose day is not yet come. Reading a popular science book on mathematics some years ago, I was amazed (briefly, and I really shouldn’t have been. It won’t happen again.) that so many ‘pointless’ theories were discovered to have practical applications, some discovered long after the theory was first promulgated (Stewart, 1998). A true application may appear later, or suggest itself immediately: the effort is not wasted.

I define number very broadly and inclusively: the integer 6, a triangle, or the algebraic notation x2, are to me number. Similarly, the word ‘happy’, Hals’ Laughing Cavalier, and a smiley icon convey the same emotional information – in informational, pictorial/geometric, and symbolic forms. Where does number come from? While I don’t want to come over all Pythagorean, I feel that number is present in the structure and ordering of the Universe. Not as a separate and discoverable entity in itself, but as our code for the otherwise incomprehensible and ineffable. It should not have surprised me that the Fibonacci Sequence can be seen in the different petal arrangements on flowers – I should have been asking how could petal arrangements be modelled, and what are the biological processes underlying the Fibonacci Sequence’s fit to the data. God may or may not play dice, but is almost certainly a mathematician.

References
Anderson, R. (2001). Detection and Representation of Oriented Contours in Human Vision. Ph.D. Thesis, University of Birmingham.
Bergamini, D. (ed.) (1972). Mathematics. 3rd ed., Netherlands: Time-Life International.
Courant, R., Robbins, H., & Stewart, I. (1996). What is mathematics?: an elementary approach to ideas and methods. 2nd ed., Oxford University Press Inc.
Devlin, K., (2000) The Maths Gene, Why Everyone Has It, But Most People Don’t Use It. London: Weidenfeld & Nicolson
Richer, É. (no date). PlanetMath [online]. [cited 12th January 2010]. http://planetmath.org/encyclopedia/NicolasBourbaki.html
Stewart, I. (1998). Nature’s Numbers: Discovering Order and Pattern in the Universe.London: Phoenix.

Foot Loose! Fibonacci

Yet another pair of socks for my mightily hoofed offspring. Ye gods I am bored with this sock business. The only thing they have going for them is that they are handy bus projects for my 10-minute commute. But I shall persevere until he has a reasonable supply – by which time he’ll probably need bigger socks – because today, for the first time EVAR, he has been willing, nay, demanding to wear something I’ve made him – yes, these socks. Ripped from my hands as I tried to finish weaving in the ends, which is nice because it’s not my favourite task, with shouts of “Mommy, put a socks on!” Guess they won’t get blocked for a while then. He pootled around the house until bedtime, when he adamantly refused to have them taken off. Half an hour after we put him to bed, I looked in on him. He was sitting on the floor, facing the window, chatting to his socks…
Again based on the Lion Brand pattern but modified for gauge as described previously, these are the Fibonacci socks I mentioned. So what’s Fibonacci when it’s at home? Well, HE discovered a sequence of numbers where each number is the sum of the two preceding numbers, hence 0,1,1,2,3,5,8,13,21, etc. So what? So, most flowers have a ‘Fibonacci’ number of petals. Fibonacci numbers also show up in the shapes of coastlines and clouds and other natural phenomena. Also, if you divide each number by the previous number, you get a result that is very close to the Golden Number/Section/Phi/Divine Proportion (1.618), whereby all sorts of The Weird And The Wonderful… ~Cue Twilight Zone music~. It’s all terribly amazing until you realise that mathematics exists to describe the universe. So it’s not exactly surprising when the universe just happens to conform with the maths, is it?

It is a little sad that this glorious stuff is too complicated to explain to kids who think maths is boring.

I have also – in two days! – completed a Valkyrie helmet for my cousin’s daughter Anna, who is a cute chubby little Brunhilde. It’s based on a Viking Girl Hat I saw on Ravelry. However the thought of forking over $24.50 for a kit had the predictable effect on my bowels, so I reverse-engineered it from the photos. I couldn’t tell for sure if there were horns or wings on it in the photos, but as a Viking re-enactor, I couldn’t in conscience put horns on it so wings they are.

I wanted a smooth, helm-like shape with no obvious decreases. To get this, I phase-shifted the decreases on each round (i.e., starting at the 1st stitch on one dec round, and on the 7th, 5th, 3rd stitch on the alternate dec round). The plaits are i-corded, though I thought about French-knitting them. In the end, though, I had the dpns in my hand, but the bobbins were somewhere in my knitting boxes…

(Modelled by my vintage fully-working Oopsie Daisy, with original outfit, for those interested in such things.)

TTFN
K