Prisoner of Benda
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.
Immortality
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.
OSME puzzle
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.
Origami and Mathematics
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.)
Coffee Stains
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.
Picture Hanging Puzzle
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.
Charles Dodgson
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.
Klein Bottle Opener
Posted by tpc at May 27th, 2010
How cool is that!
http://www.bathsheba.com/math/klein/klein_x1.html
$78 though.
Martin Gardner and that April Fools Joke
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.
Concrete Abstract Algebra: From Numbers to Grobner Bases
Posted by tpc at May 5th, 2010
is a book by Niels Lauritzen that I just checked out. My initial impression is that it is well written and contains many interesting gems. It certainly looked like a good book to teach from, although the topics covered are a little broad and thus I suspect not in enough details for a student struggling to learn abstract algebra.
One of the gems was how a computational number theorist, Thomas R Nicely, nicely found a flaw in Pentium’s floating point unit. The book provided this link to the discoverer’s site and as usual, wikipedia has a nice coverage.
Other gems include Sam Loyd’s 15-puzzle and of course the last chapter on Grobner Bases.
To the fourth dimension …
Posted by tpc at April 1st, 2010
and beyond? xkcd mentioned this game Miegakure about puzzle solving in four dimensions. I have my doubts about this but it’ll certainly be interesting.
Collatz conjecture: 3n+1
Posted by tpc at March 6th, 2010
The conjecture states that starting with any positive integer, n, map this it n/2 if n is even, or map n to 3n+1 otherwise. Iterating will eventually lead to 1.
This was a subject of today’s clever xkcd comic. It’s quite remarkable that if you google it, xkcd is the second hit after wikipedia. Pretty quick indexing, and I guess xkcd has a pretty high pagerank - I can’t check because I don’t have (like) the google toolbar.
Wiki has some good references on the problem but a really good source would be Jeff Lagarias. I remembered being interested in the problem at one point and printed out several papers to read. Of course, I had absolutely no good idea on how to tackle this. I would think that the ergodic theory guys would be in a good position to prove this.
Geeky comic
Posted by tpc at January 30th, 2010
Found another geeky comic called Abstruse Goose. Bad drawing, mathy, geeky, subversive not unlike xkcd. How to not like one who likes Abba and Star Wars?
Saw this via Juan de Mairena.
RSA 768 factored!
Posted by tpc at January 15th, 2010
Announcement here https://documents.epfl.ch/users/l/le/lenstra/public/papers/rsa768.txt.
It was done on 12 Dec 2009 using NFS.
If you visit the webpage of Laboratory for Crytologic Algorithms, part of the team that accomplished this feat, you’ll see that they actually test algorithms on a PS3 cluster. I wonder if the experiment results are ever undermined by students trying to hijack the PS3s to play games.
Bach’s canon on a moebius strip
Posted by tpc at September 16th, 2009
From boing boing, exactly what the title says.
Inumeracy again?
Posted by tpc at August 20th, 2009
I’ve been without a TV and a newspaper subscription for a few weeks and isn’t exactly up to date with what’s happening around the world. I do know that there’s some controversy again about Obama’s birth certificate. One online paper pointed out that Obama’s myspace got it wrong. He was born on 4th August 1961 and should be 48 years old this year but the page said he was 52.
Chauffeur stories
Posted by tpc at July 16th, 2009
There is this nice story that I read about Gorenstein’s chauffeur, google tells me that it came from Sarah Flannery’s book called “in code”. Below is the text lifted off the web.
“In the course of a long lecture tour, the famous American mathematician Daniel Gorenstein was chauffeur driven to various venues around the USA. While Gorenstein lectured his chauffeur sat in the back row of the auditorium. In time the chauffeur became so familiar with the material (her comments: and it was pretty deep stuff) that he joked to Gorenstein, “At this stage, I reckon I could give the lecture myself.”
One evening, Gorenstein was scheduled to speak at a small university where he guessed his face wouldn’t be known. Feeling particularly tired, the master hit upon the idea of the chauffeur to give the lecture while he would rest in the back row. The lecture went off without a hitch, at the end the chauffeur answered without hesitation all the questions, which he heard asked and answered hundreds of times before; all, that is accept for one last question which left him entirely at a loss.
After momentary panic, he composed himself and said., “I believe that question is so simple even my chauffeur could answer it.” The dozing chauffeur shamed the questioner with an immediate reply.”
Anyway, since the title of this post is in plural, there is another chauffeur story. Namely, I was privileged today to be chauffeur to none other than Serre. Can I put that in my vita?
Erdös Lap Number
Posted by tpc at June 20th, 2009
Erdös apparently liked to have children sit on his lap. See this 1969 conference photo
http://staff.spd.dcu.ie/johnbcos/oxford.htm
(There is also a young dashing George Andrews on the left.)
So it was funny to see this page on the lap number.
Unfortunately, my Erdös number is still 4. I probably could decrease it to 3 by randomly putting my thesis advisor’s thesis advisor’s name into some future paper. It is either that or wait till the apocalyse.
http://xkcd.com/599/
Another neat number puzzle
Posted by tpc at April 8th, 2009
I chanced upon this neat number puzzle devised by William Wallace, via wild about maths. It’s form is certainly recognizable, but still the effort deserves praise.
I remember a similar puzzle played with a deck of cards. You lay out the cards in rows and ask the participant to tell who which row his card is in. The trick is to collect the cards back horizontally, but deal out the next four rows vertically, this way after a few deals, you can tell which card is it.
This happen to tie in with a class I’m teaching tomorrow, maybe I’ll print out the cards and try it in class.
Breaking up is infinitely hard
Posted by tpc at January 24th, 2009
I was reading this light-hearted article by jeremy au yong in the local papers. It’s mainly about how the economy is bad and he was retrenching his girlfriend. As compensation he offered a gift.
The value of this gift will be determined by using the formula $15 x years of service + cube root of pi, differentiated over the limit of zero to infinity.
Something is wrong right? Does he mean integrated rather than differentiated, since nobody differentiates over a range. As the only variable is y for years of service, does he mean
![\displaystyle \int_0^\infty (15 y + \sqrt[3]\pi ) dy = \infty.](/blog/latexrender/pictures/3c1f7028f172be37524216119173e70d.gif "\displaystyle \int_0^\infty (15 y + \sqrt[3]\pi ) dy = \infty.")
Well, how does one pay off this infinite debt? Once again, mathematics to the rescue. He can pay his girlfriend 1 cent today, 1/2 cent tomorrow and 1/3 cent the day after …
