Walking Randomly

Welcome to this – the last Carnival of Mathematics in 2008.  Sadly, submissions were on the low side this time around – probably due to the fact that many people were away from the internet over the festive season (and so they should be).  Rather than let this adversely affect the size of this carnival, I broke every rule in the carnival book and went searching for some submissions of my own.  I hope you enjoy the results…

Carnival tradition dictates that before I start the show I should entertain you all with some mathematical facts about the number 46 (since this is the 46th edition of the carnival – for those of you who have imbibed too much festive cheer) and I have managed to come up with:

• 46 is an evil number – but only for a certain definition of evil :)
• 46 is a Nonagonal (or enneagonal) number
• The prime factors of 46 are 2 and 23 which makes 46 an example of a semiprime number and a square-free number.
• 46 is a centred triangular number.

With tradition satisfied lets look at this edition’s submissions.

Rod Carvalho of Reasonable Deviations shows how to construct polynomials from their roots using a graphical approach.  This is a nice way of viewing the process of constructing polynomials, as all the cumbersome algebraic manipulation boils down to assigning values to the nodes of a graph.

Maria Andersen of TCMTB shows how to create an answer key to your calculus test (or any other test for that matter) using Windows Journal.  I have to confess that I have not used Windows Journal because it is part of Windows Vista – something I only ever use under duress.  Maria makes it look rather compelling though so maybe I need to convince a friend of mine to lend me their laptop!

John D. Cook of The Endeavour gives us a Constructive proof of the Chinese Remainder Theorem.  This comes at a good time for me because as part of my ‘fill in the huge gaps in my maths knowledge’ project, I have been learning about congruences from an Open University booklet I found in the library.  John also submitted his most popular post of 2008 – Jenga Mathematics which is more than worthy of your attention.

If I stuck to tradition then that would be it for this edition of the carnival since they were the only submissions I received.  It seems that the festive period really isn’t a good time for getting responses from math bloggers!   So, I threw tradition out of the window and went looking for some of my favourite maths blog posts from the last 12 months.  The only rules I tried to stick to were ‘one post per blog and one post per month’.

1 year, 12 months, 12 posts, 12 blogs – Happy new year to you all.

January:  Mathematics is logical, elegant and refined.  The real world isn’t! Just like a street fight, the real world is dirty, surprising and uncompromising and solving real-world mathematical problems in physics and engineering can often take phenomenal amounts of computational power. Enter street-fighting mathematics, an MIT course that teaches you some of the tricks and techniques you’ll need in order to get approximate answers to many real-world problems in just a few lines of mathematics.  I first learned of this course from a blog post by Michael Lugo of God Plays Dice back in January and yet I still haven’t found time to work through it.  With luck, I’ll manage it in 2009.

February: I like mathematics that’s pretty and so does Vlad Alexeev – author of both Mathpaint and Impossible World.  Back in February he highlighted a sculpture of a three dimensional Hilbert curve by Carlo H. Séquin.  This post also includes an image rendered by a piece of software called Maxwell Renderer which looks intruging – can anyone suggest the closest open source equivalent?

March: Thanks to Easter, a lot of people went egg-crazy back in March and Kathryn Cramer of Wolfram Research was one of them.  In response to her initial post a lot of us attempted to create Mathematical easter eggs using Mathematica.

April: I have never taken a course in graph theory and so I don’t know much about it but I have attended talks on the subject and so have seen an old map of Königsberg several times.  Using googlemaps, the guys over at 360 showed that if we pose the Königsberg problem today then the result is completely different.

May:  If you read this blog for more than a couple of weeks then you will quickly realise that I like computer algebra systems and yet the free, open source pacakge Axiom is one that I haven’t played with much.  Alasdair of Alasdair’s Musings has though and he has also written a great 6-part introduction to the system which started in May.

June: No Carnival is complete without a puzzle to solve and Tanya Khovanova gave us a great one back in June.

July: Back in July, Eric Roland gave us details of his prime generating formula. 

August: Google isn’t just a search engine – it’s a calculator too but, like all calculators, it doesn’t always give the correct results.  Stephen Shankland gave us the details back in August.

September: Brian Hayes of bit-player invited us all to just shut up and program.  All too often I read articles from old-timers (such as myself – recently hitting 31) who lament about the loss of a supposedly golden age of computing.  You see, back in the 80s and early 90s we used computers such as the Sinclair Spectrum, Commodore 64, Acorn Archimedes and Amiga and all of them came with a programming language built in – usually some form of BASIC.  These old-timers argue that young-uns find it difficult to get into programming these days since computers no longer come with programming languages built in – or if they do then they are hidden from view in some way.

Of course this is a load of rubbish.  Hand me a computer with an internet connection and 60 seconds later I will hand it back to you with one or more programming environments installed that would be suitable for mathematical exploration (or mucking around as I prefer to think of it).  Brian’s article gives some ideas, both free and commercial, that might get you started.

October: Loren Shure of the Art of MATLAB explains how to create the Olympic rings using MATLAB.

November: What are p-adic numbers?  I have no idea – yet another subject that is on my list of subjects to study.  Dave Richeson of ‘Divison by Zero’ knows what they are though and gave a basic introduction to them back in November.  Thanks Dave – that post now represents the sum total of my knowledge on the subject.

December: Finally we reach December and a post from squareCircleZ who explains how Archimedes was doing calculus 2000 years before Newton and Leibniz.

So, that’s it.  The final carnival of mathematics for 2008.  I hope that no one minds the breaks from tradition and I hope you will join me in supporting the carnival throughout 2009.  Happy new year to you all