Walking Randomly

Hello and welcome to the 33rd edition of the Carnival of Mathematics. This carnival very nearly didn’t happen since I didn’t realise that no one had offered to host it until a couple of days ago! I toyed with the idea of letting this edition of the carnival lapse and write something in a fortnights time but then that would break the carnivals unbroken run of 33 publications (well..apart from that one time which we don’t talk about) and I simply couldn’t have that. So, with only two days to go I bent the standard carnival rules a little and started leaning on people I know in order to get submissions. After that I started leaning on people I didn’t know and I am glad to say that everyone came through and I have a nice selection of articles for you all.

Before I get onto the articles themselves, tradition dictates that I attempt to fascinate you with some interesting facts concerning the number 33. Well how about this one:

It is known that for all numbers N below 1000 that do not have the form it is possible to express N as a sum of three cubes. In other words

where a,b and c can be positive or negative. What does this have to do with the number 33? Well, 33 is the smallest such number for which a,b and c have not yet been found. If you fancy having a crack at solving this be aware that the solution for N=30 is

Anyway, enough with the trivia and on with the show!

As some of you know, I am a big fan of computer algebra systems (well most of them anyway) and so I thought I would start off with some submissions from three of the big names in the CAS world, Wolfram Research, The Mathworks and SAGE. I use the products of all three of these groups to one degree or another and so it is great to see submissions from them all. This is one of the areas where I bent the carnival rules slightly since I emailed the blog authors and said “Hi – please submit something to the carnival.” I thank them for humoring me and not consigning my email to the spam bin.

Loren from Loren on the Art of Matlab writes a regular blog on Matlab programming and her submission is a recent post entitled Acting on Specific Elements in a Matrix where she uses several methods to obtain the same result. This sort of article is very instructive when thinking about how to go about developing your code. Although she did not submit it, I thought that many carnival readers would also be interested in her post called Matlab Publishing for Teaching.

Next up from the Mathworks we have Doug whose submission is a coin tossing puzzle which he invites you to solve using Matlab. Some solutions can be found in the comments section so resist the urge to scroll down if you want to try and solve it yourself. Solving problems like this, using any system, can be a great way of learning how to use it – much more interesting than just reading through the manual; no matter how well written it is.

Moving over to the Wolfram Research Blog we have two posts in this edition of the carnival, the first of which is called Two Hundred Thousand New formulas on the Web which is a discussion of The Wolfram Functions Site. At the time of writing the site has over 307,00 formulas on it which is, quite frankly, astonishing! Pretty useful too!

Next up from Wolfram we have a blog post called Making Photo Mosaics. It never ceases to amaze me how much you can achieve with so little code – I will be having a play with this code using photos from my recent vacation :) Check out the video that Theodore has produced as part of this post as I think it’s fascinating.

Moving over to the world of open source we have a submission from William Stein – Can There be a Viable Free Open Source Alternative to Magma, Maple, Mathematica and Matlab? where he discusses the SAGE project. I have recently been looking at SAGE myself and have been very impressed with it.

This edition of the carnival isn’t just about computer algebra packages though – we also have lots of non-CAS submissions. The first of which is one from Maria over at the TCM Technology Blog where she writes about her talk, Exploring Online Calculus, at the Michigan MAA meeting. Gotta love those graphs :)

John of jd2718 asks Can we find the area of a quadrilateral from just it’s co-ordinates?, with some interesting answers in the comments section. I reckon a nice Wolfram Demonstration could be made from this idea.

Sam Shah thinks that algebraic manipulation is overrated – head over to his blog to see why. In another post, Sam also writes about some interesting calculus projects that he has assigned to his students. When I was at school I used to love open-ending projects as it used to give me a sense of ‘owning the material’. I distinctly remember doing a project on the Fibonacci sequence when I was 11 years old and spending ages on it. To this day I still have a fascination for the topic and probably always will. I wonder how often such projects can be done by school children in todays test-centric environment?

Moving on, we have Math for the Very Patient from Vlorbik on Math Ed. Vlorbik has already demonstrated his patience in the past since my blog looks horrible on his browser and yet he still reads what I have to say – thanks Vlorbik! I seem to have a problem with IE 6 that I have no idea how to fix. Just look at this blog in IE 6 compared to firefox to see what we mean. One hexadecimal pound (thats two pounds and fifty six pence) to the first person who can diagnose and fix the problem for me.

Over at blinkdagger (among other things, a great source of Matlab tutorials) they have a competition where you can win prizes from the people at the art of problem solving. There is still time to enter so take a look at BlinkDagger burgers and have a go.

If you like the level of your mathematics to be a bit higher and median graphs are your thing then you will be interested in David Eppstein’s submission Median graphs and binary majorization over at OxDE.

Denise of Let’s Play Math sent me the details of her latest post, The Function Machine Game. This is another one I remember doing when I was at school. As she suggests it’s probably best to limit the functions one can choose from – “Waddya mean you couldn’t get it – BesselJ(x) is simple!” I feel yet another Wolfram Demonstration coming on :)

Next we have a post from a blog that writes posts on the all time classic combination of subjects, cats and maths – Catsynth.com. The post is about how to calculate (that is the number of prime numbers below an integer x) without having to calculate all of the primes up to x. I wonder how the various CAS systems calculate this function? Anyone care to enlighten me?

Finally, in another bending of the rules, I’d like to present Five Open Problems Regarding Convex Polytopes from Gil Kalai’s blog, Combinatorics and more. He didn’t submit this post himself but it comes highly recommended and so I hope he will not mind having it included here.

And…that’s it for this 33rd edition of the carnival. Thank you to everyone who submitted something – without you the carnival would be..well..just me posting a load of links! Finally, would someone please volunteer to host the 34th edition of the carnival? I think it really is a lovely tradition that has been kept going by maths bloggers for almost 18 months now, which is like an eternity in internet years and it would be a shame to see it go. I think that it’s a great way of finding new math blogs and also of generating a sense of community in the maths blogsphere.

Enjoy!

Update: As it says in the comments, the next Carnival will be hosted over at 360 on May 30th so please head over there and submit a post. Making a submission is as easy as saying “Hi, what about this one…< insert link here>” 9 times out of 10 your post will be accepted so its an easy way to promote your blog.