Project Euler

Quite recently, I stumbled upon this so called Project Euler, named after famed German Mathematician. It is a collection of challenging mathematical questions.
Here is the description from the website:

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

Good luck in trying some of the questions XD

About Relativity

Quite recently I stumbled upon similar rhythmic lines describing Theory of Relativity, mainly from the book Hyperspace and A Briefer History of Time.

There was a lady of Wright.

Who traveled much faster than light.

She departed when the sky is bright.

And returned on the previous night.

Since the source are not identical, I changed it to this, without changing much of the meaning behind it.

Life goes on

Yesterday was a blast, at least not for my wallet. 08S09 peeps were as usual, the only downside is we do not have much topic to talk about. No anime, not much games, no educational debate. Almost the entire thing was dominated by NS, NS and NS. We had sushi for our lunch and unfortunately someone forget to pay me money. Hey people, I still waiting for the cash.

The movie was so so, not as exciting as the title suggest. After the movie, I went to Kinokuniya to buy some books (Broca's Brain written by Carl Sagan and another book on theory of relativity). You guys should had known why I bought those books. XD

Surprising Number Pattern

1 x 8 + 1 =9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

edit : taken from the book Math Wonders to Inspire Teachers and Students.

Interesting Pattern

Have you ever noticed this?

11^2 = 121

111^2 = 12321

1111^2 = 1234321

11111^2 = 123454321

...

111111111^2 = 12345678987654321

1111111111^2 = 1234567900987654321

and so on.

edit : taken from the book Math Wonders to Inspire Teachers and Students. 

How true is this?

When I was bored enough during maths lesson, I jotted down some prime number and find something rather surprising. Prime number that is larger or equal to 7 can be re-represented as the sum of three prime numbers. in short, d = a+b+c where a,b,c and d are prime number and d≥7.

Some example up to prime number that is less than 100 would be :
7=2+2+3
11=2+2+7
13=3+3+7
17=5+5+7
19=7+7+5
23=11+5+7
29=23+3+3
31=23+3+5
37=31+3+3
41=31+5+5
43=31+5+7
47=37+5+5
53=43+5+5
59=53+3+3
61=31+13+17
67=61+3+3
71=61+5+5
73=67+3+3
79=73+3+3
83=73+5+5
89=79+5+5
97=41+37+19

Enough of spamming out of the blue.

I Have a Dream

I have a dream
To know more about the cosmos
Seeking the truth behind its origin
And how it will end

I have a dream
To understand life better
Discovering how it starts
And how it diverge

I have a dream
To educate the world
Teaching them the truth of the universe
Out from the tyranny of religion

I have a dream
To protect the planet
That does not belongs to us
Yet we call it home

I have a dream
I will fight for it
Nothing will stop me
No matter what

Pascal triangle and number 11

When I was playing with number 11, I find a rather familiar number pattern for 11^x
we all know that 11^2 = 121 and 11^3 = 1331
121 and 1331 remind me of the polynomial (a+b)^x which leads me to pascal triangle.



Look at the number rows above. The first represent 11^0 which is 1, the second represent 11^1 which is 11 and soon on.
does this mean that 11^5 = 15101051? of course not. It should be calculated this way.


So, the answer is 161051

This method could be applied for 11^x for any value of x due to the nature of no.11

11 = 10+1

Just replace the x with 10 and the y with 1, we will get



since will always be one,




notice that can be derived from pascal triangle.

The last digit of 11^x will always be 1 when the second last will always be the last digit of x

edit: I just realised that the long equation is being cut. Since it does not affect that much, I'll just leave it that way.

McDonalds Nutrition Comparison

After careful analyzing and consideration whether it will make us full, we concluded that the best breakfast would be the hotcakes. It contains highest amout of energy, it can make you full and contains much less fat, cholestrol and sodium

For lunch, it would be hamburger ( considering you buy 2 of them) even though the energy content is about the same with bigmac, the fat, cholestrol and sodium content is much lower.

If you don't like to eat burger, you can grab 2 Apple pie, which contains about the same amount of calories with 2 hamburgers.

From the table, we can see clearly that the calory content of milkshake is more or less equivalent to one burger (average).

I suggest you guys who want to eat Mcdonalds to purchase the burger only as you might already know that a value meal contains french fries and drink. The calory content could easily reach 1000 kcal, that is half of 2000 kcal regular diet.

The datas on MegaMac can't be found in the official website. By assuming that they use the same patty, I calculated that by using the data on double cheese burger - cheese burger = beef patty. The calculated value of the beef patty will be 130 kcal, so the calculated amout of calory in Mega BicMac is 780 kcal. For Mega McSpicy, I assume that they use the same bread with normal burger. Hamburger - Beef Patty = Bread. The calculated value of the bread will be 120 kcal. The Chiken patty will be 460. WOW ! So those jokers who ate Mega McSpicy last week, beware of the Whooping 1080 kcal (without fries and drinks).

*Tables taken from McDonald's official website.
*Calculation may not be accurate.

Some old stuff from the class blog that I posted.

I'm not going for NTU

The letter had arrived, but it was too late to bother what they are going to say. I had made a firm decision to retake. I dunno why, life feel more and more depressing this few days, as if I'm carrying a gargantuan weight. It get worse each day, but I pretend it to be okay. Wednesday was a disaster. I had my weekly German tuition as usual, it was the exam week and I was trapped in the school just because of retarded sports event (that I never been bothered with since God knows). I dunno what that really troubles me now. I feels fine when I was with the CO people but it feels very awkward during normal school hours. Mr Khor was very supportive so does my Chem teacher Mrs Lee. I dunno what troubles me know.

Dad will be in Singapore this Monday, I'm going to discuss what to do next year. This will be serious, since the course that I really want is not offered in any local university, but for some reason dad decide to keep me here. June break is coming soon, dad had asked me before if I want to visit the Expo 2010 in Shanghai. Probably I'll go for it to get rid of what bugs me now.

I finished "A Devil's Chaplain" a few weeks ago and moving on "Hyperspace" now. It turns out to be a heavy book, with so many complicated mathematical concept and particle physics. Enough to make my brain melts if I rush with it. Looking at the amount of free e-books and the space left for my books, I'm considering for going digital. Yes, e-book reader. Out of so many readers it seemed hard to choose the right model and the price is not that cheap to choose so hastily. Nook, Kindle 2, iPad and Story seems to be among the best. Sadly, Kindle 2 and Nook can't be bought in Singapore (not even online). Probably I'll get Story (since iPad is too expensive) after the expiry of my Kinokuniya membership card (which is somewhere near the end of this year).

I'm working on my own notes for Quantum Physics now. It will be more detailed than school notes. Helping hands are welcomed.

Project Gutenberg

There is something interesting I find from digging LCC's blog.

Project Gutenberg, an ongoing project which is in general a digital library. Gutenberg works by transcribing old books whose copyrights have expired, and posting the books online, free for download. That's right: Anyone can download books from Gutenberg for free.

I guess that tells everything. I browsed that website only to be disappointed that I could not find a full transcription of Euclid's Elements. That bible of geometry is extremely hard to find, Google don't even have a full transcription of it. I had also checked Barnes & Noble only to be disappointed about it. It will be great if I can find commented version of the great book.

The works of Riemann is also nowhere to be find. Project Gutenberg is far from perfect, only popular titles can be found easily (BTW, isn't Euclid's Elements supposed to be popular?) such as Sherlock Holmes series, Alice in Wonderland, Homer's Odyssey, Sunzi Bingfa, some of Einstein's works, and obviously Origin of Species.

Are spiritual experiences real?

There is no absolute answer for this, since the brain is not well understood yet. However, there is a huge possibility that our brain is playing tricks. Such experiences is very personal since others might not experiences it under the same situation. Therefore, like what some scientist had said, it is self-deluding. It is personal experience, you are not supposed to draw a conclusion based on personal experience. If we treat personal experience as facts, it will be the same as treating what a lunatic had said as literal truth as simple as that.

Spiritual experiences is not caused by malfunction of the brain, it is already hard wired in the brain that we can experience such questionable thing. Drugs affect the brain by chemically stimulating parts of the brain that is linked with imagination, generating what most of us call hallucination. On the other hand, magnetic field influences the brain since the brain works by using magnetic  pulse, albeit a very weak one. How magnetic field affect the brain is still nothing much understood yet. However, once we understand much more about how the brain works, the scenario like The Brain in The Vat is likely to happen. We might be able to distort what is perceived as reality in the eye of the object.

As ethologist, Richard Dawkins had dedicated an entire chapter of "God Delusion" on the evolutionary root of religion. He argues that religion could sprung up because those who heed the words of authoritative figures have higher chance to survive in Darwinian World as they religiously follow what they are not supposed to do what could endanger their life. A child that do not heed what their parents or other grown ups is less likely to survive as he might plunge himself into life-threatening dangers. With such submission to an authoritative figure hardwired into our brain, it is easy for those in the authority to create a beliefs system as such figures usually also play the role of a sage.

Beliefs is something slowly being hardwired in our brain as generations roll. It is an evolutionary product to keep our tribal ancestors united.

Long forgotten SBQ

Source A,B and C supports the hypothesis that in 1945 to 1991 the General Assembly was ineffective in solving the problems it faced while source D and E disagrees.

Source A supports the hypothesis that in 1945 to 1991 the General Assembly was ineffective in solving the problems it faced. It state that the UN was "improperly used as an instrument of domination" with "the General Assembly...controlled by the USA". This clearly show that the UN (the General Assembly in particular) is ineffective since it had been used by USA as political tool to suppress USSR in the start of the Cold War politics with American built in dominance as shown by Source B. The source also state that the increasing membership of third world countries had led to the view that the UN is "...an organization biased against the West." The General Assembly had failed since its member view the UN as a biased organization. Since it is seen as biased organization by both Superpower who have the right to veto decisions, it will not be effective. If either superpower feels that any General Assembly Resolution is against their favour, they can just veto it. The entire discussion will hold empty result since nothing is being done to fulfill what is already decided by the great majority. The source is written in 1988, when the heights of cold war subsided to near it's end. It is likely that the author had examined Russian Archives made unclassified near the end of Cold War after introduction of Glasnost and Perestroika, thus the source is reliable. Therefore source A supports the hypothesis.

Source B supports the hypothesis that in 1945 to 1991 the General Assembly was ineffective in solving the problems it faced. It state that "...in the General Assembly, Western influence was dominant..." and the UN is a little more than "...a puppet of American government." The dominance of one party in an organization will eventually make other parties unhappy since the dominant party can do whatever they want without regard of the concern of other party. Feeling lonely and suppressed, it is a small wonder that USSR used it's veto power a lot of time during the early period of the UN before newly independent socialist Soviet-leaning states joined UN in the 1960s. It could be argued that USA bought it's political dominance from neutral states by using its economic power in form of aids such as Marshall Plan. With the entry of newly independent socialist states, it was American turn to use it's veto as USA lose it's dominance in the larger General Assembly. The Source comes from a Russian Historian who wrote it in 1955. He certainly do not know how the membership of newly independent ex-colonies will change the tide to favour USSR when he made such comment. While the source is saying the truth about UN in its early year. However, it fails to tell what happened after 1955, rendering it useless to tell whether the General Assembly was useful in 1945-1991. Overall, source B supports the hypothesis.

Source C supports the hypothesis that in 1945 to 1991 the General Assembly was ineffective in solving the problems it faced. It state that the General Assembly is "...trapped in the structural contradictions of the international system. It can not maintain impartiality..." It also state that the General Assembly is "...no stronger than the collective will of the nations that supports it. Of itself, it can do nothing." as "It can be used or developed...or it can be discarded and broken." The source clearly state that the General Assembly was ineffective as it is unable to remain neutral, it's resolution was often pointless as it is not mandatory to follow which allows members to violate it. It can be clearly seen that decisions of the General Assembly can just be thrown out of the window, not only because of veto, but also unwillingness of member states to hold it. It can be clearly seen that the UN was like a soap talk in it's early year as vetoes are cast and little political will of member nations to follow the resolutions. However, the source fails to project what happen after the speech in 1946. Even though the source is reliable, coming from the Trygve Lie, the first UN Secretary General who have first hand experience of the matter, it is not useful in judging whether the General Assembly was ineffective in solving the problems it faced in 1945-1991. Overall, the source supports the hypothesis.

Source D does not supports the hypothesis that in 1945 to 1991 the General Assembly was ineffective in solving the problems it faced. It shows statistics of the membership of the UN, where all members are part of the General Assembly It can be seen that the membership of the General Assembly increases rapidly, especially between 1945-1960 where the membership doubled partly due to rapid decolonization of Southern States. Increase in membership generally signify a success as hardly anyone would like to join an organization notorious for its failure. The increasing membership also dilutes American Domination of the UN, thus allowing the UN to work better as there is less one sided resolutions being made. Overall, the source does not support the hypothesis.

Source E does not supports the hypothesis that in 1945 to 1991 the General Assembly was ineffective in solving the problems it faced. Although it states that the activities of the General Assembly is "... torrent of unproductive and unheeded words..." which suggest the General Assembly was ineffective in solving the problems it faced since it did not bring results, the source also state that "... the Assembly performs is indeed to make all more conscious of the attitudes and interest of others and so more inclined to take account of them." Which could be interpreted as the success of General Assembly in projecting the will and interest of the world as the concern of other members is considered thus increasing  co-operation of member states as symbolized by the gathering of many people of different languages and race to address world issues, such as environmental crisis and AIDS. Since the book is published in 1979, it is safe to say that the source was the view of the author in or before 1979 which is unedited in the revised version offered by the source. Therefore, the source is reliable. Overall, the source does not support the hypothesis.

edit : Mr Lim told me that I made a huge error in this SBQ essay. I noticed it too, but it was after this essay being submitted. Can you spot the mistake?

Where The Joy of Learning Had Gone?

As a student, my life had been engulfed in education for more than ten years. It is noticeable that over the years competition do increase sharply, trapping most of us in a rat race, in order to obtain the best qualification. It often make us wonder, what had gone horribly wrong with our education system. It had been ruining the childhood of many young souls as ambitious parents (and sometimes also the school) vie with each other in an effort to produce the best student.

This very act not only threaten the joy of childhood but also true education itself. It killed the joy of learning which is the main aim if education. Instead of enjoying a good book to satisfy our hunger for knowledge, we are now desperately memorizing what is written in our notes and guidebooks for the sake of getting good grades. While our education system had been proven efficient in converting schools to a factory producing high performance students, it had failed miserably in producing students which high enthusiasm on learning the subject of their choice. It had effectively destroyed the passion of learning, by forcing students to learn everything in the syllabus. Like it or not the students have to learn a subject not of their choice, because it is simply in the syllabus and will be tested in exams.


So, what is really wrong about our education system? Why we end up studying for the wrong reason? Who are to blame for this problem? I leave it for you to answer.