Walking Randomly

One of the great things about the Wolfram Demonstrations Project is the fact that source code is included. This means that it is straightforward to take someone else’s code, learn how it works and then maybe tweak it to suit yourself. Back in February I did exactly that and used the code in Enrique Zeleny‘s Tangram puzzle as the basis for my own Valentine’s day version – The Broken Heart Tangram puzzle.

Things move on though and another demonstrations author, Karl Scherer has produced his own versions of both the Broken Heart and the Traditional tangram puzzles. Karl’s versions are faster, sleeker and generally more fun to use. As an added bonus I get to look at the source code to see how he did it – everyone’s a winner!

This morning I received the following in my email and it made me smile. It’s almost certainly apocryphal but that doesn’t make it any less amusing.

At an American university, there were four sophomores taking chemistry and all of them had an ‘A’ so far.
These four friends were so confident that, the weekend before finals, they decided to visit some friends and have a big party. They had a great time but, after all the hearty partying, they slept all day Sunday and didn’t make it back to the university until early Monday morning.

Rather than taking the final then, they decided that after the final, they would explain to their professor why they missed it. They said that they visited friends but on the way back they had a flat tyre. As a result, they missed the final. The professor agreed they could make up the final the next day. The guys were excited and relieved.

They studied that night for the exam.

The next day the professor placed them in separate rooms and gave them a test booklet. They quickly answered the first problem worth 5 points. Cool, they thought! Each one in separate rooms, thinking this was going to be easy. …
Then they turned the page. On the second page was written….
For 95 points: Which tyre?

Part of my job is to look after Manchester University‘s site license for the NAG libraries. If you have never heard of the NAG (Numerical Algorithms Group) libraries before, and if your work involves any kind of numerical computation, then I highly recommend that you check them out as they are very good at what they do. One senior researcher at Manchester referred to them as ‘The gold standard of numerical computing.’ High praise indeed and praise that I completely agree with.

The NAG libraries are written in Fortran but you don’t have to be coding in Fortran in order to use them. With a bit of effort you can call them from many different programming environments such as Python, Visual Basic, C (in fact there are C-specific versions of the libraries) and MATLAB (via the NAG Toolbox for MATLAB).

A few months ago I had a visit from some very worried looking students who needed to call the NAG libraries from Excel using Visual Basic for Applications (VBA) and they had no idea where to start. Sure, NAG have some VBA examples on their website but they assume that the reader already knows a fair amount about both the NAG libraries and VBA – knowledge that these students simply didn’t have.

I took a look at what they wanted to do and said that if they came to meet me in a couple of days time then I would put together a simple piece of code that would push them in the right direction. The code would be well commented, I told them, and would cover all of the concepts that they would need in order to put together their application. They looked very grateful and relieved.

I didn’t have the heart to tell them that I had never written a single piece of VBA code in my life!

So, off I went, learning just enough VBA to work with the NAG libraries. The staff at NAG helped me out when I got stuck and, I’m happy to say, I had just what these students needed by the time of our next meeting. I’d like to stress that I didn’t do their work for them – not even close! They told me what NAG functions they wanted to use and all I did was code up example VBA scripts that called those functions for various sample problems. This was all the help I gave them as I felt that it fell within my remit of ‘supporting the NAG libraries at Manchester’ without crossing the line of actually doing their work for them.

I looked at the pile of hand written notes that had been made while I was learning VBA and thought that they could do with being typed up. After all, I would probably have forgotten most of it by the time I was next visited by some students.

To cut a long story short, these notes ended up becoming a technical report that was published on NAG’s website today. So, if you find yourself needing to call the NAG libraries from within Excel 2003 then you might find them useful. As always, feedback is welcomed.

Thanks to all of the Staff at NAG who helped me clean up the mess that was the first draft – I have really enjoyed working with you all and hope to do so again soon.

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Update (3rd March 2009): The article referred to in this article has been updated – click here for details.

Over at Let’s Play Math, Denise has been writing about some of the search terms that end up sending people to her site and the results are rather interesting. For example, this month over 300 people found their way onto Let’s Play Math while searching for the term ‘Christmas’. Some people really like to plan ahead I guess. Other search terms that appear in her logs include things like “cute math expressions” and “ye olde math quiz”.

Denise challenged others to look through their own search logs to see what they come up with and it sounded like a fun way of passing a lunch hour so I took the bait.

It turns out that the most popular search term that gets people to walkingrandomly at the moment is ‘tangram’ since it is the top result on google images from google.co.uk. This surprised me as I think I have only mentioned tangrams once when I was talking about my Wolfram Demonstration for the broken heart tangram. The next most popular term is ‘mathematica’ which doesn’t surprise me at all as I do talk about it a lot although I am not (yet) the top search result for that particular piece of software.

So…what else brings people here according to my logs? The vast majority of the searches people used are pretty much the sort of thing I expected to see as I have written about them. Things like mathematics on pocket PC, Mathcad bugs, The Rosenbrock Function and Mathematica 6.0.3. Others were a bit more surprising though

• Walking in latex

I imagine that this particular searcher was bitterly disappointed!

• does anyone use programmable calculators anymore

Interesting question but I have no idea what the answer might be. I certainly don’t use them. Do you?

• mathworks sucks

I deal with the The Mathworks on a regular basis and, on the whole, I would disagree with this statement. Generally, I find them to be a pleasant, knowledgeable and helpful bunch but clearly this searcher thinks otherwise.

• mathematica 6.0.3 keygen

Tut tut. You’ll have no luck here, if you want to use it then you should pay for it. Use SAGE if you want (legal) free maths software rather than stealing other peoples work.

• mom in latex

I am starting to detect a trend here….

• secret math equations

Well if I told you what they were then they wouldn’t be a secret anymore.

• scary looking integrals

I plan on having a lot more of these soon.

• how free solved numericle problem in chemistry of 12th

Say what?

• gorgeous looking libraries

I do hope they found some.

• i have used full simplify to my equation in mathematica but i want to see the intermediate steps is that possible

No it’s not I’m afraid and if you could then it would not be very useful. Mathematica does maths VERY differently to the way you or I might.

• math make silver

I wonder what this person was looking for?

On the whole I am disappointed – nowhere near as many fun search terms as Denise but I did only go back a couple of months before I started going cross eyed from staring at thousands of terms. If you have a blog – what can you find in your search logs?

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A couple of weeks ago I started thinking about Valentine’s day and, since I like equations that have interesting plots so much, I wondered if I could find one that had a heart-shaped graph. A quick google search came up Wolfram Research’s Heart Surface page.

The main page described a couple of heart shaped algebraic surfaces which looked nice but there were a few more on the Mathematica notebook that the page linked to. This notebook was rather old and included plots from old versions of Mathematica so on the train ride home I wrapped these equations in some Manipulate functions and sent the resulting demo to Wolfram. The result was published today on the Wolfram Demonstrations site.

Essentially all this demo does is use Mathematica’s ContourPlot3D function to plot the curves formed from the following equations and allow you to play with the results a bit.

Nordstrand

Kuska

Taubin

Trott

Each equation is named after the person who first wrote it down (to my knowledge at least). It’s a simple demo but I hope you like it.

Happy Valentine’s day.

Welcome everyone to this, the 25th edition of the Carnival of Mathematics. The 25th anniversary of many things is usually considered to be a little bit special and is often marked by a ‘Silver’ celebration of some sort. For example, in 1977, Queen Elizabeth II of the United Kingdom celebrated her 25th Year on the throne with a Silver Jubilee celebration and the British Royal Mail commemorated the event by releasing the postage stamps below

Technically speaking of course I should have waited until the Carnival had been around for 25 years rather than 25 posts but I thought I would exercise a little poetic license here – I hope the host of the real Silver Jubilee Edition in 24 years time will accept my heartfelt apologies.

So what else is interesting about the number 25? Obviously it is a square number but did you know that it is also the smallest square that can be expressed as the sum of two squares . It is also a Cullen Number and is the atomic number of the element Manganese. Twenty-Five is also the name of a card game that is sometimes referred to as the national card game of Ireland.

Enough of the random meanderings and on with the show…

The first two submissions come from Mathmom over at Ramblings of a Math Mom who asks the question “Should gifted math students tutor others?” This is something I had personal experience of when I was at school (both good and bad) so I found her arguments interesting – feel free to head over there and add to the discussion, I am sure you will be made very welcome. Her second submission concerns probability-fallacies.

Next up we have Arvind Narayanan from the randomwalker’s journal (we have no connection other than both of our blogs have cool names!) who explains the mathematics behind part of Arthur Benjamin’s act in “Mathemagics” explained. I love this sort of stuff and may well be trying it out on some of my (long suffering) friends.

Over at Reasonable Deviations (I always think of Richard Feynman when I see that blog name), Rod presents an interesting problem in thinking about permutations. It has already sparked an interesting discussion in his comments section so why not head over and see if you can have a go at solving it? I tried, and failed, but you might have more luck.

Maria Miller highlights a link to Classic Math Mistakes over at Homeschool Math Blog which includes posters for classic howlers like “3.1hrs = 3 hours 10 minutes.” My favorite is “Finishing an exam early and then sitting doing nothing” which is clearly an elementary error when every true math geek knows that the correct procedure is to clear your throat loudly as you stand up to leave. This ensures that all of your classmates know that you have finished early and so must be better at maths than they are – just make sure that they never find out that your actual score on the exam was only 6% as it ruins the illusion.

The next submission comes from the blog of Mr Kruopatwa’s AP Calculus AB (2007-2008) class and concerns a favourite topic of mine – namely the evaluation of integrals. One of his students, Mr Siwwy (AKA Chris), asks the question ‘How “approximate” can approximate can be’ and discusses some of the elementary methods of numerical integration. In an ideal world we would always be able to come up with exact answers for our definite integrals but, as we all know, the world is far from ideal and so we often must make do with numerical approximations. Chris’ post discusses how you might start to go about making such approximations. I had not discovered this blog before now and, if all of the posts are going to be this good, then I look forward to reading more.

Over at Goods and Chattels, Amanda has been reminiscing about one of the problems from her student days in An interesting mathematics puzzle. Some maths problems seem trivial when you first read them and so you mutter “All too easy!” as you start working on them, expecting it to all be over after a few minutes. Several hours (and pieces of paper) later you give up in frustration, try to forget about it and get on with your life…but then another idea strikes you….another way of attacking it….this one might just work you know…just one more go….and it has you again. This is one of those problems. Have fun – but no peeking at the solution!

Sol’s Fun Math Blog has only been around for four months and yet it is one of the most read in the blath-sphere. Building up a Technorati rating of 88 in such a short amount of time says it all really – Sol writes stuff that the rest of us like to read and link to. His submission, “five constants tie together multiple branches of mathematics”, discusses some of the mathematics behind the equation that Feynman once called “The most remarkable formula in math”. I remember the first time I discovered this equation – my response was pretty similar to this one (don’t click if swearing offends you).

Denise discusses a quotation from Ralph P. Boas about what it takes to learn math over at her blog, Let’s Play Math. The phenomenon mentioned is something that I am sure we are all familiar with from our student (and teaching) days and her article is well worth a read. Any blog article that mentions a paper with the title “A Contribution to the Mathematical Theory of Big Game Hunting” is just begging to be read in my opinion.

What sort of calculations can do perform using nothing but your fingers and thumbs? Until I read Heathers’ article – Three finger tricks for multiplying – the best I could do was count to ten on them but now they quite a bit more versatile Head over to 360 if you want to upgrade your digits.

And now for something completely different…Rick from Big Ideas submitted an article called
Mathematical Beauty and the K₄ Crystal. Check out that gorgeous looking bit of perl – If only I could write stuff like that :)

Finally, we have a last minute submission from Brent, the author of The Math Less Traveled, who has written the third installment of his “Recounting the Rationals” series.

And – with that – I’m done. I hope you have enjoyed reading this carnival as much as I enjoyed writing it. Thanks to everybody who submitted articles – I loved reading through them all. The next carnival is over at 360 so start thinking about what your submissions might be,

Mike

On the morning of my 8th birthday my life was changed forever when I received a shiny new 48k ZX Spectrum + – the year was 1985 and this event signified the beginning of my love affair with computers. Back then the school playground was divided into two main camps – those of us who had Sinclair Spectrums and those who had a Commodore 64 and the rivalry was fierce – I even remember once being involved in a fist fight that started with a Speccy vs Commodore argument (it was probably the most pathetic punch up ever – 8 year old proto-geeks are not well known for their fighting prowess).

Of course there was the occasional oddball who had something weird like an Amstrad CPC464 (or in the case of my mate Tom – an Oric of all things) but in the main it was C64 v Spectrum and, I guess, this was my first ever technical holy war (and the only one that ended up with a physical fight).

22 years later and, like all first loves, the Speccy still holds a place in my heart but my opinions are not as polarised as they once were. These days I occasionally admit that the C64 was a good machine and, when no one is looking, I might fire up an emulator to have a game on something like the Great Giana Sisters or Wizball (the spectrum version was a bit poor you see).

One thing that I simply cannot deny is that the music on the Spectrum was just plain awful whereas that of the Commodore was quite simply stunning for its time. The sound chip on the C64 was called the Sound Interface Device (SID) and was probably the most advanced sound chip on any 8-bit home computer. Game designers used the chip to great effect in titles such as International Karate, Spellbound and R-Type – this stuff was as close as you could get to ‘proper music’ on an 8-bit computer.

Some C64 compositions are so good in fact that an an orchestra in Holland decided that they would perform full orchestral versions of them! If you head over to their myspace page you can listen to some of the results and, in my opinion at least, they are quite beautiful. What’s more – they have produced a CD with their music on it – just look at this CD Box:

Now it’s not exacty cheap – once postage and packing was taken into account it cost almost 30 pounds but I just had to order it. Expect a review here soon.