Pollock's Fractals

So you go on various news sites while you're at work and read through all the main headline news articles, procrastinating away the morning. You start off alright, with something like this...

New York Times: Obama Reiterates Desire for Comprehensive Budget Package






...buuuuuuut you end up reading increasingly unimportant articles until eventually you end up here...

http://perezhilton.com/category/kim-kardashian

It's okay. We all do it. I love a bit of Perez as much as the next girl...You go into History afterwards and delete the incriminating evidence and then scramble to assuage your guilt over reading such rubbish by finding something intelligent and 'worthy' to read.

It's always good to have quality sites in your History just in case your computer crashes and you have to call the IT guys. Just as your mother may have advised you to always wear nice underwear in case you end up in hospital (yeah... I never quite got that one either. I think doctors in the ER have more pressing things to worry about... But it's a good enough analogy in this case I guess), you should always have a nice web history in case your computer crashes and the IT guys stumble upon it.

Jackson Pollock

So read something you can be proud to leave on your web history. Pollock's Fractals is a few years old now, but as with many of Discover Magazine's articles, its fascinating subject matter is timeless.

As a side note, if you are reading fun but useless articles about Kim Kardashian and leaving inane comments on the absurdity that "this is NEWS?!" please stop. Of course it's not news, but you did click on it, so why the outrage?

Anyway, read Jennifer Ouellette's piece about Pollock's Fractals. Do it. Now. And leave me a comment to tell me what you think!

And maybe afterwards, you can catch up on what Kourtney Kardashian thinks of Kris Jenner's facelift...

Until next time, xxj

Probably the best pizza in Pakistan?

So I wonder if this holds -

P(Pizza Party is the best pizza in Pakistan) > P(any other pizza in Pakistan is better than Pizza Party)

I'm not convinced.

This is how I felt most days of my degree...

http://www.youtube.com/watch?v=SyD4p8_y8Kw&feature=player_embedded

Integration by Parts - KNOW THIS FOR YOUR HSC!!!!!

'Integration by Parts' is a method for finding the integral of two functions multiplied together. If you're doing Extension 2 in your Higher School Certificate (HSC), and in fact most advanced high school math exams for senior year students, this is a crucial rule to know. It will undoubtedly show up in some part of HSC exam Question 1, which usually deals with integration.

The integration by parts rule -


I kinda like the first way of writing it. It's just easier to say in your head and have it stick so you can just have it up in your memory for your exam. The second way with f(x) and g(x) is good when you are first learning this method, perhaps, because it helps visualise two separate functions and what's happening with these functions. It's really up to you which one you like, but I will be using the 'u' and 'v' notation rather than f(x) and g(x).

So here's an example of how to use integration by parts, and then after this example from the 2009 HSC Extension 2 exam, I will then show you where this rule came from. It's nice to see how everything connects, but honestly that is a luxury you may not necessarily have time for if you're just trying to cram in as much stuff as possible before your exams, so I have put it at the end of this post just so you can see how everything comes together and relates.



Now this is where the integration by parts rule comes from...

The product rule for differentiation!

Well, the product rule for differentiation is another rule you will have to know for your exam. If you don't know it, learn it asap. If you do know it, whew! :)

So the rule for integration by parts comes simply from integrating the product rule. Yep, that's it!

So, really, if you are in your exam and forget what the rule for integration by parts is, you can find it by integrating the product rule. I wouldn't recommend this, though. Just memorise them both. Time in an exam can be much better spent.

So here are the two ways of writing the product rule depending on which notation you like.

So if you integrate the first part of the product rule, it's like the integral is undoing the d/dx, because it's like what's the integral of the derivative of u*v? The integration and differentiation undo each other.
Any questions? Issues? Disputes? Confused? Just a bit of a Nigel and need a friend? Comment below!

xj

Google's unusual Nortel bids rooted in mathematics

Check out this article. Yay for math geeks :)

Google's unusual Nortel bids rooted in mathematics

It's so wrong to like a big corporation as much as I like Google, but I can't help it.

Does Origami Help with Medical Research?

The answer is YES it does! Cu-razy, huh?

I watched a fantastic lecture on YouTube last night (another rockin' night for me!) as part of the Museum of Mathematics channel. MIT professor Erik Demaine's lecture "The Geometry of Origami" is part of MoMath's Math Encounters series which aims to diversify and expand the general public's interest and understanding in mathematics.

You can find a direct link to Part 1 of 4 of Erik Demaine's lecture here.

The first three parts deal primarily with the relationship between origami folding and mathematics. There are mentions here and there of applications such as working out mathematically the most efficient way to fold an airbag flat in a car, but it is not until the 4th part of the lecture that he talks about really interesting practical applications relating to biomathematics and medical research.

In particular, Demaine's explains that linkage folding can be used to see how proteins in the body fold in 3 dimensions. Demaine outlines applications in research of diseases and the folding of proteins to capture bad proteins while leaving the others in tact.

So yeah, this is really great stuff, but... well it's all a bit science-y and serious.

You know when else these mathematics-based folding techniques are applied?

Designing Transformers!

www.hsctutorials.com.au

Working on past HSC papers, it's interesting seeing which years are easier and which years are harder... I have to admit, I think some HSCers definitely got screwed over. Sorry guys, but I guess that just proves you have to study crazy hard with www.hsctutorials.com.au as your main tool!

Haha. Yay self-promotion. Ain't it sweet?

Granted, the site isn't working yet... But get excited, because I'm getting there. My aim is to have videos from past papers of Extension 2, Extension 1, Mathematics (we used to call it 2 unit... it seems it is now officially just called "Mathematics" which seems silly... I digress) and General from 2004-2010 up in time for this year's HSC.

Let's see if I can get it all done... I'll keep you posted.

xj