eon

Posted by tpc at September 3rd, 2010

I used to be a member of MAA but found that it did nothing much for me except I get to issues of American Mathematical Monthly. I would classify that as good to have - something to read when I have spare time but most of the articles are not quite my cup of tea. So I decided to stop my membership after a year. The simple fact is this, as a mathematician not based in US, I do not get most of the benefits of belonging to MAA (likewise AMS.) I don’t get to attend their meetings. So why should I pay normal rates? I’m now considering whether or not to continue my membership of AMS at reciprocity rates.

However, I’ve recently added MAA to my twitter account and I have to say that they do quite a good job of pumping feeds, so much so that I have to pick and choose what I read. For example, there is a very neat article on topology and car-shades.

Posted by tpc at August 27th, 2010

Feature column on AMS website this month, using FFT to quickly multiply two large integers. Yet another useful application of Fourier transform.

Posted by tpc at August 26th, 2010

A problem from MAA website dating back to Fibonacci.

Four men already having denari found a purse of denari; the first man said that if he would have the denari from the purse, then he would have twice as many as the second. The second, if he would have the purse, then would have three times as many as the third, and the third, if he would have it, then he would have four times as many as the fourth. The fourth,if he would have it, five times as many as the first. How much denari does each man have? (Fibonacci, Liber Abaci, 1202)

Posted by tpc at August 24th, 2010

is an episode of Futurama where an actual theorem on permutations appear. Although I adore the Simpsons, I’m not much of a Futurama fan. This link explains the theorem and contains the screencap.

Posted by tpc at August 17th, 2010

I have no idea who Don Tapscott is and I probably will not read his books, but in the local papers today, he mentioned something on learning in university.

It’s not so much what you know when you graduate that counts as it is your capacity to learn all your life.

Posted by tpc at August 16th, 2010

is the title of another great story by Colin Adams in the latest Intelligencer. It’s really clever and I do not want to give the plot away but it suffices to say it is suitable for reading in the hours of twilight.

Posted by tpc at August 10th, 2010

For the 5th OSME, Erik and Martin Dermaine designed a little folding puzzle. It’s a piece of paper, with four squares at each of the four corners.

You are supposed to fold the paper such that the required four squares are aligned as below:

I finally solve the last two puzzles today while watching the news on telly, waiting for dinner.

Posted by tpc at July 20th, 2010

Recently I had the horrendous realization that I’ve lost whatever little origami skills that I once possessed. I was trying to entertain a bored child on the plane who speaks a little English, and I knew no German save “guten tag”. I thought I would fold a paper crane and I couldn’t!

Anyway, I attended an extremely good talk by Robert Lang about Origami and the connection with mathematics. A fifteen minute version is available here. (The first and last minutes are about the same as the talk, but I didn’t view the 13 minutes in between.)

Posted by tpc at July 13th, 2010

Someone said that he thinks a paper is more credible if there are coffee stains on it. Well, here’s the solution - a latex package.

Posted by tpc at July 13th, 2010

There are lots of nice videos out there which would be ideal to show to students before lectures or during breaks just to break the monotony. Here’s one about Fibonacci numbers and nature that’s pretty impressive, although I don’t think one will learn much maths from it.

Posted by tpc at July 12th, 2010

Just attended a nice talk by Erik Demaine on Origami and puzzles. He demonstrated some remarkable stuff and ended with a cute picture hanging puzzle - how to hang a puzzle with two nails such that by removing either one, the picture drops. A brief description is at the end of the following paper
http://erikdemaine.org/papers/FUN2004i_TheoryComputSys/paper.pdf
and a preprint dated 2004 that seem to be still unavailable is announced. I would love to have a look at that illusive paper.

Posted by tpc at June 14th, 2010

I’ve always loved Escher’s circle limit. Here’s a neat article attempting to reconstruct it.

Posted by tpc at June 6th, 2010

Yesterday (5th June) was World Environment Day. I wouldn’t say I’m a green fanatic but I do try my best to recycle, use the air conditioner only when it is unbearable and bring my own non-plastic shopping bags whenever I know I was going shopping. According to this webpage, a total 17,291 species are known to be facing extinction.

I wonder what is the source of the number. If you google World Environment Day 17291, 17 of the first 20 webpages has a variation of that same sentence. Out of these 17 only this one suggests that the number is not exact. I quote (emphasis mine)
“In totality, there are roughly 17,291 species that are on the threatened list”

The number 17291 stood out for me. It turns out to be prime! In fact wolfram alpha tells me it is a twin prime. No prizes for working out which is its twin. Of course, 1729 is the famous Ramanujan Taxicab number. Perhaps that’s why it looked familiar.

Update 1: Google’s spider is amazing. I just googled 17291 and this post has been indexed within 13 minutes.

Update 2: The source seems to come from The IUCN Red List of Threatened Species and this blog post has a breakdown. So the number does appear to be exact at least at a certain point in time.

Posted by tpc at May 29th, 2010

Picked up a copy of Lewis Carroll in Numberland by Robin Wilson from the library. I must admit that I browsed through it instead of reading it, picking up bits and pieces that I find interesting. For example, it is told of how Queen Victoria was charmed by Alice’s Adventures in Wonderland that she demanded:
Send me the next book Mr Carroll produces …
And the next book that arrived was … An Elementary Treatise on Determinants.

Ok, the story is not true but how cool would it be if it had been. Another fun tidbit is the following game. Starting from the number 1, A and B take turns adding a number from 1 to 10 to the running total. Whoever gets to 100 wins. What is a winning strategy? Working backwards, for B to be certain of winning, he would need to get to 89. That way, A can’t win with one turn but whatever number he picked, B can go for the win. Inductively, to get to 89, B needs to first get to 78, 67, 56, 45, 34, 23, 12 — steps of 11.

Posted by tpc at May 27th, 2010

How cool is that!
http://www.bathsheba.com/math/klein/klein_x1.html
$78 though.

Posted by tpc at May 24th, 2010

Martin Gardner passed away last week on 22 May, aged 95. Wikipedia is a good place to read about his contribution in bringing mathematics to the public. My favourite article of Gardner’s is Six Sensational Discoveries that Somehow or Another have Escaped Public Attention, Sci. Amer. 232, 127-131, Apr. 1975. (Also published in Time Travel and Other Mathematical Bewilderments.) Inside, Gardner announces six discoveries among which a counter-example to the four colour theorem. Before you jump off your seat, the article was dated 1st April 1975. Yes, it’s another very clever hoax.

The best among the six is the claim that

is exactly an integer and this fact was found by Ramanujan. The attribution to Ramanujan was clever not because of Ramanujan’s remarkable prowess of calculation but that constant is actually an evaluation of the modular j-invariant

and of course has class number one.

Posted by tpc at May 21st, 2010

If for some reason, you wanted the values of certain mathematical constants to a few billion digits, numberworld.org might be a site for you. Well known ones like are all there to billions of digits. Not much is written about the what and the how of the computations so you’ll have to take the author’s word for it. Incidentally do not make the mistake of confusing A.J. Yee, computer scientist and author of the website with A.J. Yee, the combinatorist.

Posted by tpc at May 18th, 2010

Just announced last week that solutions to the Boltzmann equation was found. It is interesting to note how it can mean quite a different thing if I had written the Boltzmann equation was solved.

Anyway, I know next to nothing about pde, so here’s the announcement.

Posted by tpc at May 11th, 2010

Learned a cool trick today. The finite projective plane of order n has
points,
lines,
points on each line,
lines passing each point.

The best known example is that of a fano plane which is of order 2. Now for order 3, there are a total of 13 lines, 13 points and 4 points on each line. It turns out you can use a standard deck of cards to represent this. You can divide the deck into 13 lines of 4 cards each, with each face value (regardless of suit) representing the same point.
Now if
,
each line is

The fun thing is to distribute the each line of 4 cards to different persons. Then you can randomly call out two face value and be sure that exactly one person has both of these cards - two points line on a unique line. Moreover, any two line intersect at a unique point - means that any two persons should have exactly one card in common.

Posted by tpc at May 11th, 2010

Cool article about Pixar and some applications of harmonic function. Would have been useful last year when I taught the maximum principle but didn’t have much else to say about it.

Moving Remy in Harmony: Pixar’s Use of Harmonic Functions
by David Austin.
via: JohnDCook’s twitter.