Tuesday, November 20, 2007

So! Since exams are over, how about we celebrate with a SURPRISE ESSAY TOPIC~

Try this for size~

Explore the themes of corruption and the nature of power in The Lord of the Rings in a coherently constructed piece of prose.

Whoever actually bothers doing a proper one (1000+ words that make sense) gets a cookie from me. For real. xD

Sunday, November 4, 2007

Mathematical Induction

The IB felt that HL Maths wasn't nerd enough. So what is? I know.

Let's create something that only exists if maths itself exists, has no real world application (besides the testing of MATHEMATICAL formulae) and is generally very, very scary sounding.

So Mathematical Induction was born (Yes the IB invented it. We're arrogant enough to know (not think, or presume, know.) that no one taught it before IB existed. Education started in 1968.)

So anyway that gives you the background of it. Mathematical Induction (from now on referred to as MI). The main point of this post is for me to consolidate my knowledge, as acting superior as when you do posts like this, it's a nice summary and refresher. So with that I've decided to minimize the hard sounding words, along with keeping the tune rather upbeat as you may have noticed (if you haven't then click here, and god speed).

So.

 

Step One - And so it begins...

Why pick MI?

Well, there are many reasons

  1. MI6 and MI5 are named after it
  2. It's pure maths
  3. It let's you prove things
  4. You don't have a damn choice noob

So now you've picked MI, and you're wondering why.

Well you're a noob, and you should of stuck with trig and pi.

(oh god I did not just do that)

Anyway.

With a mathematical formula. Eg. 2n+1 is an odd number. We can test it for n=1. For n=2. For n=3. and so on. But with just that, we cannot be sure that for n = J (Any real integer) that this would hold. So we have a slight problem.

But then along came MI. But then the traditional book explanation here gets all booky and boring and druidlike. So.

Let's go use our typical maths standby, a person flying a kite a bag with white and black balls bacteria analysis a ladder.

Let's say that our formula is a ladder. And to teach people to use our formula, we have to teach them to climb the ladder. Makes sense?

Now let's say we have something like 2 + 4 + 6 + 8 + ...  +2n.

And our ladder formula is n(n+1)

We can prove it for 1. 1(1+1) = 2

Then we can prove it for 2. 2 + 4 = 6 | 2(2+1)=2(3)=6

And hence so on. So they can go up the first step, and the second step.

But if we did it even for a thousand steps, we cannot be sure that the next step would still hold, that it would still work. (well I can, but the last time I tried to use that to justify my answer in an exam I sort of failed it)

However. If we can teach them the first step, that it works for 1.

Then we teach them how to do it for any single step (eg. k)

Then we teach them how to do it for any step after that (eg. k+1), then we've taught them how to climb the ladder!

 

Step 2 - Why that part of Step 1 works

So why is it that the whole thing is true when we just teach k and k+1?

It's an Axiom.

In a shorthand definition, it just means something that we just assume to be true.

1+1 = 2.

That's an axiom that whenever 1 is added to 1 in maths, it equals 2.

This is for our base 10 system.

1+1=10 not 2.

With a different axiom (binary) we see that it's now different.

Axioms aren't necessarily true, we just assume that they are.

So. After resisting the urge to avoid ToK (or at least a detailed discussion of it). We go into the next step.

Let's say I say today is Monday (Which at this point of time it is not)

Then if today is Monday. The next day would be Tuesday.

It is undisputable that the next day is Tuesday. But that is ONLY true if today is Monday. So Monday would be the k, and Tuesday is the k+1. This means that when k is true, k+1 must also be true.

So if k = monday

And if k is true

then k+1 = tuesday is also true

Makes sense doesn't it?

So this is the part that's often misquoted about Mathematical Induction.

So wait, you're assuming something is true, to prove that it's true?

 

Step 3 - Further explanation upon Step 2

The point behind it is, is that the k can be any figure. This means that we could prove it (or teach it to them) for the first step. Then the second step, up to the nth (or in this case kth) step, and call that bit k. Then if though maths we can prove it all the way down to k+1 as well, we can prove it for any value.

Why?

Quite simply the k+1 value becomes k, and the next value (k+2) becomes k+1.

And since the k and k+1 thing is true.

This just repeats endlessly, until you get to the number you wish to achieve.

So using the ladder example, we teach you how to get to a certain point, and then how to get from that point to the next one. Then you can just repeat the process. And you're fine.

 

Step 4 - Actual MI now (n(n+1))

Now here is the process in how we prove a MI. It's rather hard to explain without an example, so we shall use our friend n(n+1).

The start is that this series

2+4+6+8+10+...+2n = n(n+1).

The first step is to test it for 1

2(1) = 1(1+1)

2=2

So it works.

Next step is to use k.

That is

2+4+6+8+10+...+2k = k(k+1)

Now we use the next step, eg k+1

As you can see, the whole process is getting bigger by 2n each time.

2(1)+2(2)+2(3)... = 2+4+6...

So if the last step was 2(k). The next one would be 2(k+1)

So we then add this onto the previous step

So this means that

2+4+6+8+10+...+2k+2(k+1)=k(k+1)+2(k+1)

So if we look at the right hand side of that, we have

k(k+1)+2(k+1)

=k(k+1)+2k+2

=k^2+k+2k+2

=k^2+3k+2 (1)

Then this is what we got from adding k+1 onto our k value.

It's perfectly sound. Now if this value is EQUAL to the value that we get when we substitute k+1 as n in n(n+1). Then it means that the MI is true, and it holds for any integer (that we specify).

So. n(n+1) where n=k+1

(k+1)((k+1)+1)

=(k+1)(k+2)

=k^2+2k+k+2

=k^2+3k+2 (2)

When we compare (2) to (1) we see that they are the same.

k^2+3k+2 (1) = k^2+3k+2 (2)

= MATHEMATICAL INDUCTION YAY

Well that's probably the easiest mathematical induction problem you'll encounter.

 

Step 4.5 A mini step (most confusing damn part)

This is to clarify on the step that might be the hardest, from where we added 2n.

It is NOT always 2n. It will NOT be the same each time. Each one is different.

1 + 2 + 2^2 + 2^(n-1)

For our k+1 we would add 2^(k+1-1)=2^k onto both sides

1+2+3+...+n

This one is easy. We would add n, eg. k+1 to both sides.

Also a quick point on why it works.

In the first equation for (1) it is obtained by

2+4+6+8+10+...+2k then adding 2(k+1) onto both sides.

For (2), it's the next step, and hence 2(k+1) IS the next step, it gets added on.

So that means that both equations should be equal. That's why it's a proof.

Hope this helped.

If it didn't then meh.

Step 5 - A Summary and another question

So the steps are.

  1. Identify that is indeed MI (look for the words 'prove by mathematical induction' or 'using MI prove that' etc.)
  2. Now test the thing for where n = 1 to see if it actually works.
  3. Now sub k in, and assume that this is true.
  4. Now add whatever is done to the next value (see Step 4.5) to the sub'd k value.
  5. Now do some magic to it (hardest damn part)
  6. Now sub k+1 as n into the orignal formula, and see if both equations equal. If they do. Then. SUCCESS!!!

Well I think I started off rather well, but yeah, the last bit might of got a bit confusing. I think it's easier with a diagram but too lazy to draw atm.

Edit:

Btw your problem is 1+3+5...+(2n-1) = n^2

Friday, November 2, 2007

A 'Druid' Trig Question

Integral of Root(1-4x^2)dx

lol.


Thursday, November 1, 2007

One Day Left

I don't suppose I really need to tell everyone this, but like, good to know yeah...?

I have a secret cunning plan that is guaranteed* to work, and like yeah. It's quite good. If you wish to know it well... ask me on Friday :).

I'll keep this as a placeholder for now, I'll run through a Mathematical Induction (yay) in this spot later.



*99.25% of the time most of the time

Monday, October 29, 2007

A 'gtfo' Trig and Calculus Question

lol.

So.

The hour and minute hand of a clock are 2m and 3m respectively. What is the rate of change between the ends of the hands at 4pm.

GL HF

(Edit: It's not that hard if you draw a good diagram...)

A Solution to the not so 'simple' trig problem

Read the Image?
Oh Wait...

Better.

Btw Arial Lax as a web font. It's okay for text. But for a website. Severe Lackage.

Saturday, October 27, 2007

A 'Not so simple' Trig Problem

Now that we've cleared basic trig! Let's do Trig! With Integration! Yay!

Integral from 0 to Pi/4

of

(tan(x) - (tan(x)-1)/(tan(x)+1))dx

I would do it in math type, but I think that is simple enough.

Looking back at it (now that I know how to do it) it's not THAT hard, but like. How the hell was I supposed to know how to do it >.>

English Essay on Look Both Ways

Ok yay, second essay in a day (oh shit, it's 3am, not a day then...)

Umm... Hopefully this turned out better than the last one. Time limit still way out, I think I need to work on somehow getting rid of distractions while keeping the computer. Is that even possible? At least the word count is more reasonable now.

My quotes definitely need work... Had to force some into it, probably very obvious where I did too >.< class="MsoNormal">

Edit: Titles are FTW

Part 2

Look Both Ways shows that despite life’s trials, happiness is possible.’ Discuss.

Happiness is one of the main themes explored in Sarah Watt’s award winning film Look Both Ways. The concept of being happy is an abstract one in a film preoccupied with other more powerful and overshadowing themes such as death and fear. Every character in the film is exposed to some form of these ‘trials’, random chance events that have the power to destroy lives. Look Both Ways explores the possibility of characters maintaining happiness despite the events that seem to have the ability to destroy any reason to be happy, and ultimately take control of lives. Some such events that might prevent happiness in the film include cancer, fatal accidents and deaths of those close to us, as well as the wider implications and people affected by each of these events, some perhaps not first-hand. However, Look Both Ways is a film which proves that happiness is not based on the difficulty of life trials, but on the strength of the human spirit that ultimately dictates the possibility of happiness. This is shown through some of the key characters in the film: Meryl, Nick and Julia.

Meryl provides an excellent example of someone who has been traumatised by her experiences with death, especially in her family. Her father’s death left her floundering and disorientated, such that her own view of life and death became distorted and fatalistic, making trite comments such as “maybe it was meant to be”. Combined with the impact of watching a man get run over by a train in front of her, her mental health has severely been damaged, made evident by the flashes of paintings that signify her imagination, filled with morbid scenes of her own death played out in countless different scenarios. She is buffeted by these bouts of paranoia and fear and “seeing death everywhere”, unable to face the world without being plagued constantly by images of her own death. Meryl seems to be completely dominated by her fears, scarred from the loss she experienced. However, despite the dreary circumstances Meryl faces, Look Both Ways is a film about hope and victory. We are shown that happiness is not dependant so much on external forces beyond our control, but rather on the strength of the inner character. Meryl realises through a chain of events together with Nick, her coming to terms with the death of her father and the accident she witnessed depended upon her own true acceptance of her circumstances. Only upon her actual submission to the fact that “things just happen” could she finally begin to regain her happiness, signified by the final photomontage at the end of the film.

Nick is another main character in the film who is subjected to the powerful forces of random events, termed life’s trials. After he was diagnosed with cancer on Friday, in response to his legitimate question “How long do I have?” he is told that “the specialist will see you on Monday”. Nick was left with nothing but his wandering, troubled mind, left to its own devices for an entire weekend, all the while harbouring the fear of this cancer that he has been told he has contracted.. After the sentence was passed by the doctor, unhealthy “speculation” is the only thing he has left to do, waiting impending doom. Happiness is probably the last thing on Nick’s mind at this stage, as his preoccupations and fears about cancer all billow out and take control over his mind, will and emotions. Despite this, the end of the film and the cathartic rain that falls symbolises hope, and Nick finally learns what it means to depend on the “light to show us the next footstep”. Nick eventually realises that he cannot fight the cancer, “then there’ll be more I don’t know”, and so in finally letting go of this inhibiting burden, and “face his own death”, he is able to take up happiness again, once again evident from the photomontage at the end of the film, where he even recovers from his cancer.

Julia is more of a peripheral character in the film; however her story ties in strongly with the centrifugal force of the film, the local train accident during which her husband perished. The loss of a loved one is a difficult one indeed, emphasised by the director in the extreme close-up shots of Julia’s face, showing the extent of the grief and devastation she experienced. In this sense, she is not dissimilar to Meryl, but they differ in their individual expressions of the grief they feel. The deep-set sorrow felt by Julia is something constantly referred to with film techniques throughout the film to alert readers as to the significance of this as a theme. After the initial shock of the death of her husband, Julia is approached by the train driver, who offers an apology in the form of a card. Julia is also offered a choice here, she could continue to dwell in her despair or accept what’s happened as unchangeable and random, and begin the journey to regaining her happiness, a door which the apology opened. Julia in exchange offered her forgiveness, freeing not only the train driver of his burden, but also of her own. By forgiving someone for the indirect loss of her spouse, she has already sown the seeds of redemption and happiness in her soul. Her husband’s death did not change, but what underwent the change to enable happiness to bloom again was her own mindset.

Ultimately, the characters in the film Look Both Ways learn that happiness is not necessarily something influenced totally by external events, but can also be engineered in them. Despite the rigorous trials of life, characters show that it is still possible to obtain true happiness independent of outward circumstances, proving that it is more a state of mind than an actual factor that they too cannot control. It can therefore be concluded that happiness is actually very much in the minds of people, able to be unearthed if it is called for by someone, regardless of their current situation, environment or difficulty they face.

Find the Maths Formula!

Edit: I wrote the generic formula right, but the actual results wrong... So yeah. Updated Numbers!

Yay fun! Find the relationship between the following numbers!

0 3 7 13 21 28 36 43

I think I might have posted this before, not too sure. Also, if it's too hard, I'll post a few more numbers after it. I made this sequence up in a Chinese Exam I believe, and (for some reason) it's written into my Physics book. So yeah

(And use the god damn tags people). Just push Show All. I've entered every relevant tag.

Friday, October 26, 2007

[Essay] The Kite Runner

So yeah, this is the first essay I've written this year for the expressed purpose of practice alone.

It was a disaster.


It went way over time, way over the unspoken word limit, and is probably largely a jumble of nonsense. Future essays should be better, please don't get turned off reading them -.-"

I just felt like it would be a waste to delete it, so i'll just post it here.

Part 1

Baba sighed, “It may be unfair, but what happens in a few days, sometimes even a single day, can change the course of a whole lifetime, Amir.” To what extent was Baba prophetic?

Khaled Hosseni’s novel The Kite Runner is one full of twists and turns, especially in the lives of his characters. It epitomizes the transient nature of humanity, and how quickly and suddenly the “course of a whole lifetime” can be redirected or shattered, simply by the presence or occurrence of one or two key events, that could take place in but a single day. Amir’s life is repeatedly subjected to these key events, events that shape and reshape the course of Amir’s life, his mindset, and ultimately his values. During Hassan’s rape on the day he won the kite running tournament, Amir’s inaction in response to that horrific act left him and his conscience scarred for life. Amir’s consequent set up of Hassan and Ali, in another selfish act to purge himself of his wrongdoing by attempting to rid himself of Hassan, resulted in both his and Baba’s devastation at the loss of people who symbolised a part of their childhood, their life. Rahim Khan’s call, convincing Amir to return to Kabul to “redeem” himself was another turning point in Amir’s life, leading up to his eventual confrontation with Assef, the catharsis of the novel in a sense. All these events, most of them arguably unfair, took place in the space of no more than a few days, yet each holds more significance in Amir’s life than the rest of it together, based on the author’s portrayal of this character. Baba’s statement holds true throughout the novel with respect to Amir’s life, and may be considered highly prophetic.

The first of the key events in Amir’s life, and possibly the most significant, was witnessing Hassan’s rape as a bystander, while doing nothing to stop it. Throughout Amir’s childhood, Hassan has been portrayed as a loyal servant, yet at the same time, a friend to Amir. His Hazara birthright dictated that this would be his place in society, and he accepted it graciously, serving Amir, a wealthy Pashtun boy, with all his heart, despite their similarity in age. Amir treated this pseudo-“friendship” with a certain degree of contempt, likely due to the fact that at the same time, Hassan was his servant, less educated, less worthy than he was. What he yearned for instead, with greater passion than anything else throughout his childhood, was the acknowledgement and “Baba’s love”, something which he felt was not present in sufficient quantity in his life. The fact that Baba showed uncanny interest in the well-being of Hassan, his servant, did nothing to relieve Amir of this burden in himself. When the time came and the strength of the bond between Hassan and Amir was tested, it is clear that while Hassan chose his Amir’s acknowledgement in exchange for his own welfare, Amir would not do the same for Hassan, who “[was] just a Hazara. I should not be expected to defend him”. While Amir obtained his father’s love from the kite which Hassan risked his life to protect, Amir clearly cannot overcome his resulting strong conscience and sense of morality, and could only temporarily “[forget] what [he] had done”. In the space of a day, Amir’s conscience from then on was forever pitted against him, for an unfair choice he was made to make as a young boy. This is what sets up the direction of Amir’s life henceforth, triggering an unstoppable chain of events. The irony of the time it took for such a significant change to occur is perfectly exemplified in Baba’s prophecy.

As a result of Amir’s actions, he could no longer face Hassan due to the weight of his guilt and regret that he carried from that day forth. Amir’s utter remorse towards himself resulted in his mentality warping, to such a point where it was impossible for him to live together with the boy who symbolised both his childhood, and his guilt and shame. In a fit of arrogance and desperation, Amir framed Hassan with the act of stealing, one which Hazaras took very seriously among themselves in relation to themselves. Ali was forced to take Hassan and leave Baba’s service, on his pride and honour as a servant. The once proud Baba was left shattered; bitterness was rife in Hassan and Ali, who both knew of Amir’s treachery right from the beginning. Amir was left alone in a void, alone in the “depths of [his] pain”, only able to regret and grieve for his own foolishness as his conscience berated him for the rest of his life for the “blackness of grief [he] had brought on everyone”. Amir’s betrayal of Hassan, Ali, Baba, and ultimately himself once again took no more than a whim to come to fruition, corresponding to Baba’s prophetic words.

Much later, when Amir was a married, middle-aged man living in America, having escaped Afghanistan before the strife brought by the Taliban began, Amir is still haunted by his actions as a boy in Afghanistan. “Steel hands closed around [his] windpipe” upon the mention of Hassan is strong evidence that Amir has been unable to leave Hassan and his past sins behind, instead carrying them inside himself. It is only after Amir is settled in his life in America that Rahim Khan, an old friend of Baba, calls him with a proposition: “a way to be good again”. Rahim Khan implied in his call that he knew everything that Amir had been ashamed about, and Amir’s decision was a difficult one, whether he should continue covering up his past or face his shame and guilt back in the “city of hare-lipped ghosts”, which he eventually chose the latter because of the pull of his conscience, and flew back to Pakistan and Kabul to face the “ghosts of [his] past”. The simple phone call by Rahim Khan resulted in some very deep-set and complex emotions in Amir being triggered, ultimately altering his life’s path altogether simply by convincing Amir to go to Afghanistan.

In Kabul, the plot reaches a catharsis when Amir is forced to confront Assef in a fight to take Sohrab, Hassan’s son, back, foreshadowed by the confrontations he had with Assef back in his childhood. Sohrab represented redemption and hope to Amir, the key to reconciling his past sins and guilt of how he wronged Hassan. As Amir was getting beaten by Assef he felt a sort of purging as a result of it, a “sense of peace” and “healing”. Amir felt that this beating was what he deserved as punishment, and it gave him a new level of emotional freedom, as he had never experienced since “the winter of 1975”. The moment of calm and joy Amir experienced changed him forever, and from then onward he felt as if he could finally forgive himself for the wrongs he committed against the now late Hassan. He took Sohrab into his care after rescuing him, the embodiment of hope and new lease of life in Amir’s life. However, the actual process of ‘restoring’ Sohrab was one that took a lot longer than a short period of time. Even at the end of the novel it is clear that Amir and Sohrab’s relationship is by no means complete or even close. This is proof that not all significant events happen in short time frames, but can take up to whole lifetimes to “melt the snow”, “one snowflake at a time”. While it took only a few moments for Amir to regain the peace and tranquillity within himself, he will probably spend the rest of his life continuously making up for Hassan in the form of his relationship with Sohrab.

The Kite Runner is proof of the volatility of life and direction in people and characters, and the power and significance of “what happens”. Baba’s prophetic words have been repeatedly proven true in the novel, especially in his own son Amir’s life, that it only takes “a few days” for life to undergo complete transformation. However, this is not always the case for all life-changing events, and many of them may take a much longer time to come to terms with or accomplish.

An Answer to Nucleic Acids

For the first part of this answer, please see the comments section of the question post.

Ok, here's a diagram of a basic DNA molecule that might help put some stuff I said in context.



EDIT: Please go look at the original image on photobucket itself (view image/drag and drop to address bar/whatever (for those of you who don't know >.>)), cbf rearranging/resizing it to fit this space.

This basically shows a double-stranded DNA molecule with some of the bonds present, also maybe make things easier to see.

P = Phosphate (circle thing), which I talked about earlier. It forms a sort of backbone along the spine of the DNA strand, as you can see.

S = Sugar (pentagon thing), which I also talked about earlier. In this case the sugar would be deoxy-ribose, since this is DNA. Bonded to P by a phosphodiester bond.

A, T, C, G = Nitrogenous Bases = Rectangle things. Yeah, these were what I was talking about, as you can see they are hydrogen bonded to their complements on the other strand of DNA.

Ok, few things I missed. T and C (U also) nitrogenous bases are actually called pyrimidines, a group that basically means single ringed structure. A and G are purines, meaning they have a double-ringed structure (much like caffeine~). For some reason, the hydrogen bonds between G and C bases are stronger than A and T, don't ask me why now, cbf. Probably just remember that.

Also, DNA strands are always bonded in opposite directions to each other. So one strand is upside down compared to the other when they are connected, symbolised by the 5' (5-prime) and 3' (3-prime) ends opposed to the 3' and 5' ends of the DNA strands. Just a side note, DNA and RNA can only be synthesised in the 5' to 3' direction. If you need more details on DNA/RNA replication please comment. Actually, comment anyway.

If you need more details on the actual structures of phosphate, sugars and bases, I will (not) draw them for you... Actually I can't really remember them. Lol, oh well. I bet your chem textbook/data sheet/google has it.

Yeah, anything you still need just put in the comment~

PS I think this is sort of helping my bio lol. Hooo~

EDIT #2: The poor kittens :'(

Thursday, October 25, 2007

A Question on Nucleic Acids

So, after 10 papercuts, blunt scissors and running out of glue, I present to you this question.

Can anyone here go through a basic (yet detailed) summary of Nucleic Acids, mostly in relation to Human Biochemistry.


[Essay] I'm Not Scared (Emily)

Well, this isn't mine, but SOMEONE (ahem Emily) is too lazy to post on this blog (probably too lazy to read/use as well)

So I'll post it for her.

I assume its for I'm Not Scared.

“Papa is the bogeyman.” Is Pino Amitrano an evil man?

In the novel I’m Not Scared, Pino Amitrano is portrayed as the villain who committed a heinous crime and betrayed his son. Pino was a man of principles and integrity who loved his family whole heartedly, yet somehow he was overcome by greed and fear which prompted him to do malicious acts which made him evil man. Through various events that took place in the novel, Niccolo Amanniti showed how he descended into darkness enabling him to commit an evil sin of kidnapping Filippo and later attempting to kill him.

At the beginning, Pino was described by Niccolo Amanniti as a short but strong man who cared deeply for his family but this was later proven otherwise as the novel progressed. He was shown to have high family values as he treasures the times he has with his family. His loving side was shown through acts of giving and humour as he bought gifts for his children and joked with his family. He bought Marie a new pair of glasses and a “gondola” for Michele. He took back his role as the head of the house whole when he told Teresa not to worry about fetching the water and that he would go instead of the kids. “…I need to get something from the van anyways…” He all showed his fathering side when he played “soldier’s draw” to settle a little argument between Marie and Michele. Through these little gestures of affection, it does not seem like his is an evil man, however this was proven otherwise when he ignored Michele’s explanation as to why he was late. He had totally shut Michele off and told him to “get out”. His anger was the first sign of his capability for evil. He used vulgar words towards Michele “…what have you been rolling in...you smell like shit…” which further enforced his capability to inflict evil upon others in particular Filippo and Michele.

As the novel progressed further, Pino’s capacity to inflict evil up on other become clearer when Michele found Filippo and made the connection of this discovery with his father. The condition that Filippo was in is further proof that Pino is an evil man. Filippo’s skin was “…caked with mud…eyelids were sealed with blood…lips were dark and split…All his teeth had gone black.” Pino and the adults of Acqua Traverse treated Filippo like an animal and an item of trade. They did not give Filippo enough food, starving the boy in a dirty whole. They fed him scraps from home, for example the meat that Marie did not want to eat. They gave him just enough food to sustain his life long enough to complete their transaction. Pino further showed his capacity for evil when he confronted his son and blackmailed him into not visiting Filippo again. “…swear that you will not go back there…swear on your fathers head…if you go back….these people will kill him and it will be your fault” It was harsh of Pino to endowed such a heavy weight upon a nine year old child’s shoulder. Apart from this, Pino also tried to buy Michele’s silence buy purchasing a new red bike for him. Pino’s naïve thinking destroyed Michele’s innocence. He has mentally and physically harmed both his son and Filippo. He had betrayed Michele when he did not stand up again Sergio “…felt like I had been stabbed on the side…papa was the boss of Aqua Traverse” and then showed Michele his capability to harm when he said “Two ears we’ll cut off. Two.” His ability to be so cold and uncompassionate destroyed the respect Michele had for him as well as his innocence. At the end of the novel, Pino’s full capacity to inflict evil was shown when he set off to kill Filippo. He had lost the game of “soldier’s draw” and had become the executioner. However, there was a twist to the ending where he did not shoot Filippo but his own son. The fact that he shot the bullet shows that Pino is in fact an evil man.

Niccolo Amanniti captured every aspect of Pino’s character, vividly demonstrating his capability to inflict evil through various events. Pino chronically descended into darkness, which clouded his judgement thus destroying his principles as can be seen throughout the novel. His moral values were eroded by his greed, fear and desperation. It was his self destruction which made him and evil man.

Wednesday, October 24, 2007

Actual Solution to 'Simple' Trig Problem

Using a totally non-stolen picture*

*Using Microsoft terms**
**Disagreement with these terms will result in your computer having 'mysterious' BSOD whenever you try to complain, or in extraneous circumstances***
*** Eg. When we feel like it.

Super Edit:!!! I just realised as I did this problem, that the picture indeed IS wrong. The 3 and 5 (cm) are in the wrong positions. If you swap them Around, it's okay. So the picture IS wrong. Swap the 3 and 5 around ok.

So now, I've got to draw it in Paint.


So. I suppose I'll do it in Mathtype.

It's a bit small, but that explains everything I suppose.

What a fun problem huh?


Tuesday, October 23, 2007

Solution to 'Simple' Trig Problem

Ok, this took me ages to figure out, trying various methods and stuff and getting all messed up. I even had to get help from David himself, who seemed to know a formula that I didn't but was expected to know for this question. Fine, so I fail at basic trig. Maybe I just suck, I'm no match for evil IB HL people.

Anyway, this is a diagram (which I'm hoping real hard that it's right)




Erm... The answer I got at the end was approximately 10.88, please tell me if this is right or wrong and therefore whether I should bother showing what I did.

Cheers.

Saturday, October 20, 2007

English Essay

A commentary written on a Prose (Aprox 1000 Words)

Ok I lied, more like 850 words. I felt like I really failed at this commentary, I'll tell you what mark I get as I'm sending it in to the teacher as well.

The passage from The Loom seems to be about the isolation of a mother, the hobby that she finds, and the use of it as an expression for her feelings. From the very start there seems to be a sombre mode present in the poem, and we first find out about the isolation from when ‘we dig her out’ she juts ‘crawls back in, only deeper.’ It is presumed that the mother goes into this isolation because of an external pressure, because she seems to ‘have taken refuge’ in it. It appears as if that the mother seems to be unable to communicate properly to the daughters, and they are unsure about what they should do in relation to this situation.

The use of three sisters seems to represent three different views on what they should do about this situation. Two of the sisters, are at opposites in view points, with Jo wishing to ‘break through’ to their mother, to talk to her, while Linda ‘defended the fortress’ that she was in. However it was the middle daughter, who provides a compromise to their situations, giving their mother a loom, which allows for communication, at their mother’s pace. There is the use of two of the sisters to present widely divergent views, while the one in the ‘middle’ often viewed as a mediating role, provides the solution to their conflict.

One of the most obvious themes in the prose is the use of colour to represent different things, both in the life of the mother, and the pieces made from the loom itself, seemingly comparing the pieces made from the loom as a snapshot of the life of the mother, or more accurately, of the lives around the mother. The first colours that are presented are brown and neutral shades, the ‘colours she preferred’. However later on she discovered that she could pick up threads selectively, so that she could show ‘flashes of colour’ or ‘never show it at all’. Even if it wasn’t easily apparent at the start, or even visible at all, if the piece was turned over, ‘the colour would still be there’, just not apparent in the ‘right side of the fabric’. This seems to draw a parallel with the mother’s ways of expressing, at the start, seemingly only showing feelings about herself, separated from the rest, the dull browns and neutral shades. Yet through the loom she is able to display her true feelings, not large overt ones, but one’s that seem to only peek through, appear as a flash, but if feelings could be turned over an examined like the pieces from the loom, would end up ‘startling the eye’. The feelings were there, just that she was incapable of expressing them, or perhaps more precisely, that the daughters themselves were incapable of understanding them completely.

This is further illustrated by the fact that when Jo, the sister that wished to break through directly, receives a muffler, she regards it immediately as ‘Mom’s colours’, perhaps without disdain, but without the immediate appreciation of the colours in it. Sharon, who seems to understand their mother better then Jo, asks her to put the muffler on, and then was surprised as ‘light, hidden colours leaped from the brown fabric’. She then states a phrase, one of the most important in the poem, ‘You’d never know it unless you looked real close’, to which Sharon replies with perhaps the most striking phrase in the passage, ‘Most people don’t’. This seems to symbolise the fact that even though it is not apparent at the start, it is still there, and that most people tend not to notice this fact.

The flashes of colour that is apparent though her weavings are reminiscent of periods in her life, each representing different things. There is the grey, for the cold mornings, when she warmed clothes for Jo, brown for the lunch and the brownies that they had made. White was the colour of sheets, while blue was Cathy’s favourite colour. Even though all of these colours are part of her life, every one of them are also connected to her daughters, which, as these would be important memories, show that they are important to her. This is emphasised through the fact that she loves weaving, and ‘never misses a class’, with the only exception being when ‘her daughters are home’.

The final few parts of the prose seem to suggest that their mother is not as strong as their father, as ‘she was crying’ when Jo had to leave. Also she is described as a ‘lighter mass’, one which gravitates naturally ‘toward a more substantial one’. She then returns home, and once again ‘amidst the comings and goings of the live around her’ she is by herself, a ‘woman bent over a loom’. In this she slowly weaves her pieces, which is synonymous for the lives around her, and of her life. Perhaps devoid of other ways to express herself, she continues weaving these images of live, ‘weaving the diverse threads of life’ into a ‘miraculous, mystical fabric’ which expresses her true feelings and views.

'Simple' Trig Problem

Honestly if you can get this (even though it's not that hard), you've understood all the basic theory behind trig. Some of the more complex stuff (ie. complex numbers, pun non-intended) aren't included.

In triangle ABC, b = 2theta, c=theta, AB = 3cm and AC = 5 cm. Find the exact area of the triangle.

It appears simple. But it takes a damn long time.

Thursday, October 18, 2007

Definition of Literature

The slow accretion of detail that gives the reader something to do is the hallmark of literary writing. The knowledge that there is more to know the more the writing is experienced contrasts with the smooth superficiality of pulp fiction which leaves the reader no decisions to make because their sympathy is unambiguously directed by the writing. literature describes an event or character in a way that honours the complexity of experience. And this makes commentary writing possible.


With this, I shall post a commentary soon. Hopefully.

Btw, since the essays/questions/whatever will be huge, the rss ----->>
Is prob your best bet for finding new things.

[Question] Let's get this started: Vector Proof hooo~

Ok! Study blog, yay! So, this is the first post of this blog relevant to it's use I suppose.

David did mention that it was for anything and everything pretty much, so I'm going to kick this off with a super disgusting vector proof question.

(Those doing spec, if this looks familiar, check your textbook _b)

Here goes:

The points A and B have position vectors a and b respectively, relative to an origin O. The point P divides the line segment OA in the ratio 1:3 and the point R divides the line segment AB in the ratio 1:2. Given that PRBQ is a parallelogram, determine the position of Q.

Gl, hf~

Submissions on this blog itself as a post would be great ^^, although I'm kind of scared how it's going to turn out as a post... Diagrams? Try photobucket.

I will attempt this question too, and will eventually put up an answer if no one bothers (assume I still care enough).

First Post & A guide

As I make this post, I do stress the fact that I'm on caffeine, tired, had a headache for the last 3 hours, and I am sick of calculus. Whining aside (if you do want more, clicky or clicky2), (and now the free advertising aside), we begin the first post and a guide.

The purpose of this Blog is for us, to submit work (mostly English essays), and have them reviewed. Questions can also be put up, along with other things. Comments should be made in the comments section (sigh).

Umm, as a Format, I would like it if you put either, Question, Guide, or Essay, and also the subject area. But if you don't I'm not gonna yell at you or something -_-. Just easier that way.

So yeah.