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

Interesting article from the NY Times this week...

This is a really interesting article. I certainly can imagine this becoming an increasingly important idea in education. I certainly wish I had had these sorts of programs, particularly in high school, to build up my instincts when it comes to maths. Amazing. I wonder just how far-reaching the application of this style of learning could be... What do you think?

Brain Calisthenics for Abstract Ideas

http://www.nytimes.com/2011/06/07/health/07learn.html?_r=1

Just because sometimes I need a break from math stuff...

My latest fad is a desire to buy a plot of rural land and set up a large luxury safari-style tent, solar shower, hobby farm etc. I think I will definitely need to rig up a swing like this and bring a long flowy dress so I can sit in the countryside and do the whole boho ethereal thing as I ponder recursion theory...

Yeah, yeah, roll your eyes. It's all good, I'm used to it :)

Fashion and Hyperbolic Geometry

I only did one semester of Topology in my degree. We got straight into homeomorphism and sat around laughing away (in science professor from The Simpsons type laughter) about how a topologists can't tell the difference between a cup of coffee and a donut because they are homeomorphic. Hardy har har.

But, um, if I'm going to be completely honest, I had NO idea what the point of it was. Yeah, it's kind of fun and at various points quite trippy, but when was I ever going to use this? How did it relate to other areas of mathematics?

Of course, I should have asked the lecturer. But I was just trying to get everything in my head, do it all correctly, pass the exam. Worry about "the point of it all" later, right?

Yeah... Probably not the best way to go through university. So I'm taking the time to try to piece everything together now...

The more research I do, the more I realise just how much I've forgotten and how much I need to re-learn, but I did come across this article which was fun and interesting.

Maybe its time I had my nonna teach me how to crochet so I can make myself some hyperbolic pants...

http://discovermagazine.com/2006/mar/knit-theory

Mmmmm, pi....

TriBeCa Film Festival

So I saw 'Revenge of the Electric Car' at the TriBeCa Film Festival last week. Loved it. It's the sequel to 'Who Killed the Electric Car?' from a few years back.

Follow the link to read my blog post about it below. Just another one of the many interesting career paths involving maths and science. If I hear "Ugh, when will I ever use this?" from a student one more time... !!!

http://addingbliss.typepad.com/adding-bliss/2011/04/how-jess-spent-her-week-week-7-attending-the-tribeca-film-festival.html

xxj

Pi Day

I know it's really sad, and I shouldn't admit this to anyone, but I really can't wait for it to be March 14, 2015!

Now, this only works if you write the date USA-style with the month first. Since I'm living in New York City at the moment, it totally works :)

March 14, 2015...

3/14/15

Yep... PI! 3.1415...

Sadly, I have pi memorised to some ridiculous number of places. I won't write it out here. It's just too too nerdy even for this no-one-reads-me math blog. I had a friend in 6th grade who was just such a know-it-all and kept going on about how she had memorised all these digits of pi, so I decided I just had to beat her. Yep, put me on in a sports team and I have no idea what's going on and don't really care who wins, but challenge me to a pi dual and I'm all over it like a fat kid on a cupcake. Totally kicked her ass by the way. Yeah... Just sayin'...

She went on to graduate high school two years early and has just finished med school, while I'm still boasting about my success back in 6th grade... on a blog that no one reads... Oh dear.

Xx

Yep...

I remember a particularly grueling Number Theory lecture where the chalk boards covering the front wall (numbering 9 in total on rollers so they could slide up and down the wall) were totally covered in really dense proofs and crazy symbols. At the end, the lecturer was about to erase the boards but decided against it when he saw the next class was for first years. The looks on their faces as they walked in and saw what was in store for them in the years to come... Classic!

I imagine a couple of people transferred to Arts after that...

My blonde moments...

Story of my life. I always manage to follow up any smart thing I do or say with something completely ridiculous like this... Luckily people generally put it down to having a "blonde" moment.