Archive for the ‘General’ Category

The Angel Problem

March 20, 2011

Go to http://library.msri.org/books/Book29/files/conway.pdf. Read the proof of Theorem 3.1. Am I being ridiculous if I believe it to be incorrect?

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I’m done.

February 1, 2011

From its start back in May 2010, this blog has been one big failure. It took me over half a year, but I finally realised that I

– Can’t write
– Can’t present math in a clear fashion
– Can’t be bothered to write posts on a regular basis

At least these things are all true when the language I use is English. So, if Chewbacca lives on Endor, I must quit!

Probably, this implies that I will start a new blog sometime in the future. That could be in a few months, but it could also be in a few decades, I dont know. When the time is ripe, I will let you know. That’s a promise. You might ask why I would want to start a new blog, ever, given the above three reasons why this one failed. Well, because I can say that I learned a lot from this blog, so I can confidentially assert that my writing will be better next time.

Catch you on the flipside.

Random update

November 23, 2010

The reason for the fact that is has been more than 2 weeks since my last update is simple; contrary to popular belief, I have been busy. With a few things actually. I have been a bit busy studying (who would’ve thought). I have been busy writing my first article (thank you very much), which will be finished end of the week, hopefully. I have been busy playing guitar (obviously, I suck). And, last but not least, I have been juggling like there was no tomorrow (again, I suck). When I’ll improve, I might put some videos of me juggling here. That ought to be fun 🙂 My personal bests are, as of this moment:

3 balls: 12 minutes (close to 2500 catches)
4 balls: 57 seconds (over 200 catches)
5 balls: 15 catches
6 balls: 6 catches
7+ balls: err, no

I’ll update you on all of these things as soon as I’ve got some news.

EDIT 25 november: Woohoo! I flashed 6 balls 😀
EDIT 30 november: I updated a few personal bests. As of tomorrow I won’t do that anymore to be able to track my progress. But right now I’m too happy with my clean run of 15 😀

An elementary proof of the irrationality of Pi

June 29, 2010

I´ve been wondering for a while now if it exists and if so, how it looks like. By elementary I mean something like: completely (elementary) number theoretically. Because I know there are a few easy proofs that \pi is not rational, but all of the ones I’ve seen, make use of some calculus (like computing an integral or so). So, my question: Can anyone show me the irrationality of \pi with just the very basics of number theory or tell me  why it is/shouldn’t be possible? For example, a few years ago I tried to prove it using the the formula: \dfrac{\pi}{2} = \displaystyle \sum_{k=0}^\infty \dfrac{k!}{(2k + 1)!!} along with basic arguments which you may find in some proofs of the irrationality of e = \displaystyle \sum_{k=0}^\infty \dfrac{1}{k!}. Although (obviously) I wasn’t able to prove  the desired result, I did not find a reason why it shouldn’t be possible in principle. Even more, I had the gut feeling I was almost there. So I might give it another shot it the future, but hopefully that doesn’t stop you, my dearest reader, from helping me if you’ve got some info on this.

All your linearly independent spanning sets are belong to us!

June 17, 2010

(for the ignorant) Yes yes, I own zhe matrices! At last, I, think I, passed my Lineair Algebra-exam. And since I’ve got 5 more exams to learn in the following week, (probably) no more updates until I finished them all. Bai bai

The Number Game (2)

May 26, 2010

My laptop and I haven’t been together for some days now, so I couldn’t update you on my interesting life. But apart from being sleep deprived, cycling the elfstedentocht and (probably) not being able to pass a lineair algebra exam, because of sleep deprivation and pain everywhere, not a lot happened. So, basically, all I have to tell you is:

2^{45} * 3^{13} * 5^6 * 7^2 * 11 * 13 * 17 * 19 * 23 * 31 * 47

Good luck!

Nailing my life

May 21, 2010

Some days are just plain motherfucking awesomeness. Like yee-esterday. And by yesterday, I mean the past 30 hours, because I kinda screwed up my sleep rhythm. Let me tell the stories.

One of the first things I noticed when I woke up (approx 8 pm on May 19th), was an e-mail from mister Nicely, telling me that my proof was correct. That is, I showed that for every integer k > 1, an integer x exists, such that: \displaystyle \frac{x}{\pi(x)} = k, where \pi(x) is the prime counting function. Since I proved that fact (it definitely does not earn the title ‘theorem’) about a year ago, I was quite surprised to see it as a conjecture of Golomb on Nicely’s site. So I e-mailed my proof, and it got posted. While this could easily be considered a trivial story, and that claim has merits, I’m actually quite happy about it. Because I not only proved the above fact, I also proved my existence! Furthermore, I started thinking about the math in question some more, and I came up with the following conjecture, which, to me, seems certainly true: for every positive integer m, there is a positive integer k, such that there are at least m different positive integers x, for which \displaystyle \frac{x}{\pi(x)} = k. Maybe even the following is true: for every positive integer m, there are infintely many positive integers k, such that there are exactly m different positive integers x, for which \displaystyle \frac{x}{\pi(x)} = k. The second one seems quite hard (maybe the case m = 1 is doable), but I thought about my first question some time, and I think it should be attackable. I (think I) am able to proof the conjecture, under the assumption of Hardy-Littlewood’s prime-k-tuple-conjecture, if we drop the condition that k is an integer, but only want it to be rational. Although I must add that I haven’t written down the details yet. I might put my thoughts on it here. Butttt, obviously not now, because I have to tell you the rest of mah story!

So, by (what felt like) morning, I was already world-famous. Then my calculus-teacher e-mailed me. And that event was something I had been dreading for like a month. Because I asked him to e-mail my grade on the exam and I wasn’t quite sure about it. Because, honestly, I HATE CALCULUS. And I’m obviously talking about the way it’s taught and the fact that you won’t be allowed to come back ever again if you use your intuition for something. I mean it’s good for students that have never seen proofs before and shit, but come on, be less trivial, puh-lease. Honestly, I might roundhousekick the next person who asks me to prove that \displaystyle \lim_{x\rightarrow 0} x = 0 straight in the face. Or, somewhat more generally I guess, the next person who uses the words ‘epsilon’ and ‘delta’ in one sentence. And this hot, raging anger I felt inside me, made it almost impossible to open my book to study without hysterically crying. Add this to the fact that I usually only get part marks  (I mean, what’s up with that?), when I answer a question like ‘prove *something trivial*’, with ‘that’s trivial’ and it becomes clear why I was scared that I failed my exam like a little bitch. As it turns out: I PASSED. Go suck on that you Cauchy!

And these 2 major steps towards eternal glory made me

1) call my lovely little sister for like 40 minutes
2) able to help out a friend (which wasn’t even math-related)
3) impulsively (though wisely) decide to buy a new phone
4) notice that it was like the most beautifullest weather ever today
5) write a post that has (ugh, too geeky) \lfloor 200*\pi \rfloor words in it

The Number Game (1)

May 15, 2010

It’s time for something geeky. I’ll post a number, you ‘guess’ why it’s cool. Obviously, this is, in essence, subjective, so you might question the existence of a wrong answer, but I’ll try to make it as clear as possible. So when I say ‘1729’ and you answer ‘that’s a cool number, because when you reverse its digits, it’s the zipcode of my aunt’, you’re just wrong ;). Because everybody knows that 1729 is the second taxi-cab number. Otherwise known as the Hardy-Ramanujan number. Alright, an easy one to start us off:

11011000001

I’ll post an interesting number once a week. Also, when you comment, could you please hide your comment if it contains (possible) information on the solution, so as not to spoil? A simple way to do this is to use the colour white; 

<font color=”white”> Your text should be here </font>

But there might be a more advanced way. Anyway, happy puzzling!

Help

May 15, 2010

Alright, fuzzy story, clue can be read below. So far I’ve done the following if I wanted to post something: Type the post in \LaTeX, copy/paste the post here, put $latex-signs everywhere to tell WordPress you’re using \LaTeX, and done. However, today I realised how wrong this is. Apparently, and this is something I should’ve known, but didn’t, WordPress isn’t able to work within environments that, in \LaTeX, say ‘change from normal text to mathematical text and do something beautiful (like aligning equations)’. Because when you want to use \LaTeX in WordPress you have to put a $latex-sign in front, like I said, but Wordpress then automatically thinks that you’re writing math, so it changes to math-text. So you can’t tell WordPress that you want to change to math-text, because it already assumed that! But that also implies that you can’t use environments that tell \LaTeX to go from normal to math text. Wow, that was even fuzzier that I thought it was going to be.

Long story short: I’m not able to display equations as neat as I want. In particular, the thing that tilts me the most is my inability to align equations. So I searched the forums, but no help. Then I started to try random stuff, didn’t help either. The best I was able to do, is something like the following:

\begin{pmatrix}a^2+b^2&=&c^2\\&=&d^2-e^2\\&=&(d+e)(d-e)\end{pmatrix}

which, in a very basic way, resembles something that, when I really want to see it, looks like it’s not insanely far from what I might want. But in any case, it just feels ridiculous to put equations in a matrix.

So: please please please help me. Either by telling me how to use the align-environment, without WordPress realising it, or by telling me that the above is, in fact, the best I can do, or by convincing me that it doesn’t really matter that much how math looks. Go!

EDIT: I found a way to do it, but that is like a hell. So if you have anything useful to say, please, still comment.

First Post

May 11, 2010

  The first line of a brand new blog usually kinda sucks. I know, right?
Ok, to the point; I have a few reasons to write this blog. First of all, if I start arguing with myself about my incapability of being a good student, I usually lose, mainly because I just lack good arguments. Math is just what I want to do now, it´s what I would love to do when I´m old, so why am I not studying my ass off? But now, when that little guy in me starts ranting again, I just say ‘dude, busy blogging, man’. And I win, for once. Second of all, which is kinda related to my first of all, I really really really want to be a mathematician some day. And I noticed that all the people that write math blogs, are mathematicians. So one easily conjectures that anyone who starts a math-related blog, almost surely becomes a mathematician. And because I’m highly susceptible of being a counterexample, I myself am the ideal check of this, intuitively obvious, conjecture. Alright, what I’m trying to say is that this blog, while possibly being some form of procrastination, also has the great potential to be a way of motivating myself. Third of all (and yes, this first post is just a way of convincing myself that this blog is an awesome idea by naming all the reasons I can think of. Semi-interesting posts will appear later, maybe), sometimes I have these plainly brilliant thoughts, only to write them down on a piece of paper that gets instantaneously lost. Writing them here makes sure that these ideas won’t get lost and, even more, allows other people to read and mock them. Win, win win.

And yes, odds are that this post will be the only one I’ll ever write. Odds are that I will be the only one, who will ever read this post. But, let’s face it, odds are also that I’ll walk outside my apartment tomorrow, make a turn and bump into the love of my life. So, basically, the only thing I can do is to actually walk around the corner and hope for the best.

Ps.
Wow, that was one cheezy analogy. But then again, it’s cheezy, ’cause it’s true.