Inspired by Flix’s chemical jewellery, I did a little Googling and found these beauties:
Earrings inspired by hyperbolic geometry (as discussed on the site to which the image links)
String parabola earrings on sale at Etsy
Möbius strip earrings? Je pense que oui!
And a rather gorgeous yet I-dread-to-think-how-expensive necklace with fractal patterns
I must admit, it’s the Möbius strips which would win me over!
There are many reasons why I’m quite fond of my Maths Teaching module, but one of them is that it contains summative work – namely coursework that actually counts towards 50% of the module*. Some of that was a learning report based upon lesson observation that we did last term**, but the higher percentage of the marks come from this term’s essay and presentation.
Our brief is very general. We have to take any second year degree level material (- probably Maths but not necessarily) and discuss the links between that and the teaching of school Maths. It should be aimed at teachers primarily, but with a secondary school student in mind in terms of application to learning – which obviously allows a huge amount of scope for interpretation and the opportunity to create our own project around what we are interested in. The presentations have already started happening, with people talking about what they have written – or intend to write – in their essays; just as disparate examples, topics so far have included ‘The significance of prime numbers’, ‘The Maths of Poker’, and ‘Maths in Indigenous Cultures’.
I want to do mine on matrix transformations – and more particularly on the visual interpretation thereof and why it’s a helpful approach to take to the learning of Linear Algebra, a very fundamental part of Maths which has applications in just about every branch you can care to think of. In order to do this, however, the essay itself is going to require a certain level of graphical input.
There’s the tried and tested drawing by hand followed by cut-and-paste approach, of course. But the potential for things going wrong, particularly when I get into three dimensional figures, is really quite high, and this is the 21st century after all. So as the geeks among you might have predicted, I started playing about with ways to do things digitally. Tester challenge: to draw a transparent unit cube, based on its vector co-ordinates.
First up was Maple, the program I used extensively last year for Numerical Analysis. It took hours of frustration to achieve this:
, which actually doesn’t look bad in the program itself. But my, was the coding messy, and my is the graphics quality poor, even when you think you’ve got it nailed by using PrintScreen rather than exporting as a JPEG. And I don’t think you can make GUIs*** in Maple, which was my next inspiration for an active demonstration of how this could be applied to teaching.
So there was really only one way to go. MATLAB. The ultimate powerful mathematical programming language, which I have no idea whatsoever how to use, but from what I do know of it would be perfect for this sort of thing. I spent three hours in the IT labs this afternoon, combing the Help sections while trying not to be overwhelmed by the sheer amount of stuff that I could never learn in a year, never mind a couple of weeks. But eventually I found what looked like a useful function, and after a bit of tweaking came up with this:
Much crisper, much tidier to code, and more to the point, much easier, potentially, to manipulate in the ways in which I want.
It’s only the start. I have yet to work out 2D plots. I have yet to work out how to write a single function producing such a figure, and GUIs are a mile away. But it’s a start. And it’s amazing how much easier I’ve found it to get down to some sort of ‘practical’ work.
x
*”So what?” I hear you cry. Well, every other Maths module (apart from the final-yr project module) rests 100% on a three-hour exam. And, y’know, I miss coursework! Even essays, ‘cos they now hold something of a novelty value.
**Which in my case occurred six days into taking fluoxetine! Score.
***GUI = Graphical User Interface – ie. something on the screen which a user can click or enter text into, and then it links to the code to produce a visual output. Basically like every bit of software we normally use (without needing to know the coding behind it). I created one in Java in that first-year programming module that I did, and it was a remarkably satisfying experience!
I bought this material in a lovely little fabric shop in Durham a few days ago:
Having got it home and inspected it in a more natural light, it really is quite bizarre! In different lights it ranges in colour quite dramatically. It’s slightly stretchy and has a lovely soft velour/suede-like texture, but it’s also quite lightweight and nice and drapey. It was one of those impulse buys (which I’d promised myself to agree to before going browsing that morning. Within reason of course!), the upshot of which is that I didn’t have a particular pattern in mind for it and am now wondering what to make!
So after a considerable amount of browsing around pattern sites, I have narrowed it down to the following options…
1. Something along the lines of this:
, although possibly without the hole at the back of the neck as that might get quite irritating. There are loads of twist top variations upon a theme out there, but I do quite like the construction lines of this one and Jalie patterns do have a reputation for being well-designed and nicely fitting. Might look a little odd in the material though, I can’t tell.
x
x
2. Or this:
Nice tunic design – I’d probably do the long sleeves from view C and wear it as a jumper (ie. with another top underneath). My hesitations with this one are whether it would suit me – whether it would come too low in the chest area and whether it would hang too loosely, even with the tie. Sorry about the image quality.
3. And then again there’s this:
, which is just that bit different. It involves binding, which I’ve done before, and bust darts, which I haven’t and am mildly terrified of – but all in the name of learning, eh?
x
x
x
So! You’ve guessed it! Opinions please :-)
As a partial response to a Facebook conversation I am currently having with Jenny, may I present to you a swirly tailed, single round eared, three-legged and bearded mouse? This one has no tummy button, in which it is lacking somewhat.
x
(Original source. Excuse the cringeworthy blogging style, if you will. It’s amazing what you think of yourself from an older and questionably wiser perspective..)
Maths is a beautiful subject.
I was attempting earlier to persuade Maple to plot the evolute of an ellipse (with a = 9 and b = 6, for those who care. I could have put in a couple of extra lines of code and written it for arbitrary a and b, but to be quite honest I couldn’t be bothered). For an ellipse like this:
xxxxx, it’s meant to look vaguely like a diamond-shaped hyperbola. Instead I got this:
xxxxx, which is clearly complete rubbish but rather pretty nonetheless if you excuse the poor graphics quality of this particular example.
As a related aside, I was giving up in the library for the day and copying the code via Microsoft Word into an email so that I can play with it here at home. Word thought about the text for a long while before solemnly declaring that it was Spanish (International).
It’s been that sort of a day.
Recent Comments