eon

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 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 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 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.

Posted by tpc at May 8th, 2010

Being down under results in the privilege of receiving my copy of the Notices of AMS five months late. The December 2009 copy showed up in my mail last week and the best article of all is about Legendre. It seems that despite being such a famous figure in mathematics, the mathematical world had been using a wrong portrait of him until recently. Everything came to light only when a computer search revealed that two different man named Legendre shared the same portrait. Full story available online.

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.

Posted by tpc at March 11th, 2010

It’s really quite good. Here is a chinese translation of an article by John D. Cook. I have no idea who did it but it certainly does not read like it was done by a machine. For example the chinese version did not try to translate the key phrase “just in case” and “just in time” - thus losing some points for artistic merit - but used the literal meaning. Now feed the article into google translate and do a line by line comparison with Cook’s original article and you’ll see it works very well.

What’s interesting is how errors often made by chinese-speaking people when they using english, surfaces. For example the second half of the first sentence:

literally in chinese is “You will learn what?” Of course we do it should be rendered as “What will you learn?”

Another example:

was translated “This is because there are too many really do not need things.” A better translation might be replacing “really do not need” by the word redundant, or again by switching the order around “too many things that are not needed.”

So it seems that some work need to be done to come up with a good inanimate translator. The differences like noun followed by adjectives in French need to be taken care of when translating to English.

Posted by tpc at February 24th, 2010

I thought I would have written something about wolfram alpha when it was released but a search of the archives brought nought. I was reading an MAA magazine and found a new trick. You can actually find word subsets. Yes, I’m aware that of the very clear internet anagram server which is an anagram of “I, rearrangement servant.”

Anyway, here goes. Hmmm… atheist is a subset of mathematicians, but an immediate corollary says that theist is also a subset!

Posted by tpc at January 22nd, 2010

Every now and then I bump into some obstacles that made me glad that I spent the first two years of my undergraduate days in the now defunct computational science program, learning programming on linux machines. Add to that some experience with perl during my first job, using vi or regular expressions is not entirely alien to me. The obstacles mainly have to do with collaborating with people who work on linux.

The most recent one being sharing a tex source file, which when ftp-ed from linux to windows, ended up with a ^M character at the end of every line. The stupid tex editor (winshell) on the office pc couldn’t recognize it, treated it as a newline and as a result wouldn’t compile.

Some googling found the following solution in vim

:%s/^M//g

To get the ^M in vim for windows, type Ctrl+q+m. In unix it is, I think, Ctrl+v+m.

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.

Posted by tpc at June 18th, 2009

I got myself a hp tx2 tablet running on amd Turion with 4GB ram. A dear friend helped me upgraded to vista 64 bit in order to fully utilize the ram. I tested it against the desktop running xp 32 bit on pentium core 2 duo. I was told that this desktop actually has 8GB ram but xp 32 bit only recognise 3 GB.

It was not a rigourous test by any means but I got both systems to try and factor

(3)(5)(17)(257)(641)
(93461639715357977769163558199606896584051237541638188580280321)
(5704689200685129054721)(59649589127497217)(1238926361552897)
(67280421310721)(6700417)(65537)(274177)

Anyone want to verify the computation?

It took 2141 seconds on the notebook which, according to the software, utilized 2.3 GB but 2300 seconds on the desktop which utilized 2GB. So it’s probably the memory that made all the 10% difference.

Posted by tpc at September 24th, 2008

While perusing some blogs, while waiting for the rain to stop, I’ve found more evidence to support learning maths than replying on calculators.

A TRAFFIC warden gave parking fines to innocent motorists – because he did not know how to tell the time.

The bungling parking attendant had to use a calculator to work out the expiry time on tickets displayed in motorists’ windscreens.

But with calculators working in decimals rather than minutes and hours, the ticket-happy warden had his book out before realising his maths was letting him down.

One of his victims was IT manager Dave Alsop, who tried his best to show the warden the errors of his arithmetic ways. But to no avail.

The 29-year-old from Torbay had parked in the Terrace car park close to Torquay harbour and paid £1.20p for 75 minutes. His ticket was issued at 2.49pm and would have covered him until 4.04pm.

But when he returned at 3.41pm, he discovered he had been given a £50 parking fine.

He found the traffic warden nearby and asked him why he had been booked when his ticket clearly showed he had time remaining.

The warden disagreed and tried to prove his point using a calculator.

He tapped in 14.49 and added 0.75 to produce a total of 15.24, which he claimed meant Mr Alsop’s ticket expired at 3.24pm – 17 minutes before he returned to his car.

Mr Alsop said: “I tried to explain to the warden but he didn’t have a clue. He thought he was doing things correctly. He just carried on doing other cars parked there.”

The warden insisted he was right and issued fines to two other unsuspecting motorists.

Mr Alsop, who works for Pavey Insurance brokers in Torquay’s Abbey Road, appealed, had his fine waived and received an apology from Torbay Council.

Via -> Natural Blogarithms -> 360 -> God Plays Dice -> Eric Berlin

Posted by tpc at June 10th, 2007

Found a very nice post by Alane Tentoni on the topic, together with a link to a great story by Asimov about a future where people cannot do maths without a computer.

via Carnival of Math IX

Posted by tpc at March 15th, 2007

Picked up this book from and library. I particularly liked this paragraph:

Intuition, in the Star Wars sense, may be the most important and most ignored part of our machine-oriented world. When do you look beyond the rational, the routine, to see what is really around you? Trust your feelings, your “instincts.” In science, you need to know when your equipment isn’t working properly. We’re obsessed with high technology, yet a few bad sensors can cause the meltdown of a megawatt nuclear generator, and a small chunk of foam insulation can destroy a billion-dollar space shuttle and its crew. Skywalker, strong in the Force, knew when to use his computer and when to ignore it. Do we?

And how do you develop this intuition in maths? By immersing yourself in it, by working through pages and pages of calculations and certainly not through using fancy-schmancy calculators!