There isn’t much information about the course online yet, apart from the brief description on the official website and this AV-services-tastic trailer:

Since everything to do with popular maths has to pun (see also: literally any other page on this site), I can only assume that the course will end with the construction of a robotic hand or high-friction surface.

Tony Croft has a good pedigree with online learning resources: for many years he’s been in charge of maths support at Loughborough, including the invaluable mathcentre support site.

*Warning: this post has like a bajillion animated GIFs in it. Your internet connection will suffer.*

*Mathbreakers* is what I’d call an ‘edutainment’ game, though I think that term’s fallen out of favour. The developers, Imaginary Number Co., say it’s “a video game that teaches math through play”. It’s aimed at school kids, and deals with basic numeracy.

Anyway, it’s a third-person platformer/shooter in a world full of numbers. Bubbles containing numbers are your tools for defeating knocking down walls, operating machines, and defeating monsters.

You’re given several weapons, each of which does different things with the number-bubbles. First of all, the core mechanic is that throwing one bubble at another adds them:

Bubbles are scattered throughout the world. If you mess up and lose them or misuse them, it doesn’t matter because the original bubbles are replenished after a few seconds. That means that you’re free to experiment, and also that you need to know what you’re doing to solve a puzzle rather than just scattering bubbles around and trusting to luck.

The second weapon is a gun which shoots ten copies of any bubble you pick up. I’d be surprised if anyone didn’t immediately, on getting the gun, try to make a ridiculously big number.

It seems that 32999 is the biggest number allowed, and the addition operation becomes non-commutative when you get near to it. Why not just pop bubbles that get too big?

A rocket launcher adds a bubble to every number within a large radius:

Finally (as far as I’ve seen), there’s a sword which chops bubbles in half. But see if you can spot the deliberate mistake:

Again, I’d prefer it if the $\frac{1}{65536}$ bubble just disappeared when you cut it with the sword. You can get a $\frac{1}{2}$ bubble very easily by starting again, so why does the division wrap around?

I hope that the wrinkles in the game will continue to be smoothed out by further playtesting. For example, I was confused by this floating question mark when I first came across it…

… but it turned out that the message was referring to this lift a few metres away, which raises or lowers to a height corresponding to the number you put in its funnel.

Another little niggle is that the numbers in bubbles and other elements are often quite hard to read. The refraction shader on the cubes is particularly misleading:

But aside from all this, I had fun with *Mathbreakers*, and I’m not even the target audience.

Of course, all this maths fun secretly exists to teach children arithmetic, and games which attempt to do that abound. But most “fun with maths” games, *MyMaths* included, provide extrinsic motivation: do the maths, and then you get a reward. In *Mathbreakers*, the maths is the game, and the reward for doing it is more maths. Heaven!

*Mathbreakers *comes with a dashboard for teachers using the game in class, similar to that offered by systems such as Oxford University Press’s *MyMaths*. You can track students’ progress through the levels, and assign levels to individual students. Imaginary Number Co. has also created a few lesson plans on topics such as addition and fractions.

More information

*Mathbreakers* is available for Windows and Mac. The “full game” costs \$15, or there’s a “deluxe edition” which comes with access to the lesson plans and a level editor for \$50.

Generals gathered in their masses,

Just like witches at black masses.(Butler et al., “War Pigs”,

Paranoid, 1970)

Brummie hard-rockers Black Sabbath have sometimes been derided for the way writer Geezer Butler rhymes “masses” with “masses”. But this is a little unfair. After all, Edward Lear used to do the same thing in his original limericks. For example:

There was an Old Man with a beard,

Who said, “It is just as I feared!-

Two Owls and a Hen,

Four Larks and a Wren,

Have all built their nests in my beard!”(“There was an Old Man with a beard”, from Lear, E.,

A Book Of Nonsense, 1846.)

And actually, the practice goes back a lot longer than that. The **sestina** is a poetic form that dates from the 12th century, and was later perfected by Dante. It works entirely on “whole-word” rhymes.

A sestina has thirty-nine lines. The main (and mathematically interesting) part of the poem consists of six stanzas of six lines each; there’s then a three-line *envoi*. I wrote a sestina for the 2013 MathsJam conference; the full poem, in all its dubious glory, is available on request, but here are the first two stanzas:

One Saturday, with gladdened heart I gaily rise

And greet the Autumn morn at this unwonted hour

With strong black coffee’s aid, I slowly come to life

I shower, shave and dress, bolt down some bread and jam

Pick up my case; take laptop-holder on my back;

And then anon to Turnpike Lane direct my steps.At Euston station, as I ride the rolling steps

That seem to mumble, groan and mutter as they rise

I muse: it is another year, and we are back!

As time goes by, it seems it quickens by the hour

The world’s events now seem to cluster, crowd and jam

Accelerating as they touch my fleeting life.

As you can see, the rhyming happens not within stanzas but between them. The six “rhyme words” that appear at the ends of the lines of the first stanza also appear in all the others. The words are the same, but the order is different: they’ve been *permuted* from stanza to stanza. The same permutation is used each time, so all in all, the rhyme scheme looks like this:

Or, more abstractly:

This permutation is most easily studied by focusing on its inverse, which is given by

\[\delta_6(u) = \left\{\begin{array}{rc}2\,u,&\quad 1\le u \le 3,\\13-2\,u,&\quad \text{otherwise.}\end{array}\right.\]

This inverse permutation (and therefore the original permutation) has order $6$: that’s to say, ${\delta_6}^6(u) \equiv u$ (and ${\delta_6}^n(u)$ is not equal to $u$ for any value of $n$ smaller than $6$). Moreover, it’s a **complete cycle**: the sequence

\[1, \delta_6(1), {\delta_6}^2(1), \dots, {\delta_6}^5(1)\]

goes through all the numbers from $1$ to $6$. It’s this feature that makes it work as a rhyme-scheme.

Sestinas aren’t unique. There’s such a thing, for example, as a **quintina**, the main part of which consists of five stanzas of five lines each. The quintina’s rhyme-scheme looks like this:

This corresponds to the inverse permutation:

\[\delta_5(u) = \left\{\begin{array}{rc}2\,u,&\quad 1\le u \le 2,\\11-2\,u,&\quad \text{otherwise.}\end{array}\right.\]

In general, we can talk about the $n$-tina, and its inverse permutation:

\[\delta_n(u) = \left\{\begin{array}{rc}2\,u,&\quad 1\le u \le n/2,\\2\,n+1-2\,u,&\quad \text{otherwise.}\end{array}\right.\]

But not all $n$-tinas make good rhyme-schemes. That’s because the permutation isn’t always a complete cycle. For example, in the case of the **ottina** (which, if it existed, would consist in the main of eight stanzas of eight lines), the permutation looks like this:

As you can see, it consists of two disjoint cycles of order $4$ (namely $(1842)$ and $(3756)$). This means that the permutation itself has order $4$: our poem would have the same order of rhyme-words in the fifth stanza as in the first (for example).

The **settina** ($n=7$) is even worse. Here’s its permutation:

This resolves into the cycles $(1742)$, $(36)$ and (worst of all), $(5)$: the fifth line’s rhyme word simply stays the same from stanza to stanza! Overall, the permutation has order $4$, which doesn’t even divide the number of stanzas, $7$. This would be spectacularly unsuitable as a rhyme scheme.

The literature on sestinas somtimes calls values of $n$ for which the $n$-tina permutation is a complete cycle **admissible numbers**; this struck me as a little uninspired given the subject matter. Elsewhere, they’re called **Queneau numbers**, after the poet and mathematician (yes, really) Raymond Queneau, who seems to have been the first to pose mathematical problems about sestinas. In my MathsJam talk, I opted to break with this terminology, and instead call such numbers **sheerly poetic** (which allows us to say that numbers like this exhibit the property of **sheer poetry**).

It’s known that $n$ is sheerly poetic if and only if the corresponding permutation has order $n$. Now, this isn’t true of permutations in general: for example, the permutation $(123)(45)(6)$ has order $6$, but it isn’t a complete cycle. However, within the restricted class we’re interested in, all permutations of $n$ elements that are of order $n$ really are complete cycles.

Here are the first few sheerly poetic numbers:

\[n=1,2,3,5,6,9,11,14,18,23,26,29,30,33,35,39,\dots\]

They might not look all that familiar. That changes, though, if instead we note that

\[2\,n+1=3,5,7,11,13,19,23,29,37,47,53,59,61,67,71,79,\dots,\]

and indeed it’s known that if $n$ is sheerly poetic then $2\,n+1$ must be prime.

This actually isn’t that hard to prove; contact me for details! The proof, like that of nearly all theorems to do with $n$-tinas, makes use of the fact that modulo $2\,n+1$, the inverse permutation $\delta_n$ always corresponds either to multiplication by $2$ or to multiplication by $-2$.

But you’ll notice that some primes are missing from this list. For example, $17$ is certainly prime, but as we’ve already noted, $8$, equally certainly, won’t *quite *do as a value of $n$ to build a rhyme-scheme on (though it wouldn’t be as disastrous as $7$). So the converse of our theorem is false: if $n$ is sheerly poetic, then $2\,n+1$ is prime, but not necessarily the other way round.

So let’s call $n$ **merely poetic** if ${\delta_n}^n$ is the identity: that is, if the order of the permutation (or, equivalently, its inverse) *divides* $n$. If $n$ is merely poetic but not sheerly poetic, then you could write an authentic $n$-tina, as long as you didn’t mind the rhyme-scheme repeating itself a bit; at least, when you came to the end of your $n$ stanzas of $n$ lines, you wouldn’t be in mid-cycle.

Now, according to this definition, $8$ is merely poetic (permutation order $4$, which divides $8$), but $7$ isn’t (permutation order $4$, which doesn’t divide $7$). It turns out (and this is also known) that if $2\,n+1$ is prime, then $n$ is merely poetic (and may be sheerly poetic). Once again, the proof uses the fact that the inverse permutation $\delta_n$ corresponds, modulo $2\,n+1$, to multiplication by $\pm 2$.

Which would be quite tidy, except that the converse of this theorem is false as well. That’s to say, there are merely poetic numbers $n$ for which $2\,n+1$ simply isn’t prime. The first few of those are

\[n=170, 280, 552, 864, 952, \dots,\]

corresponding to

\[2\,n+1=341, 561, 1105, 1729, 1905, \dots.\]

Those values of $2\,n+1$ may just possibly be familiar to some; they have quite a special property. They’re all *pseudoprimes to base *$2$: that is, they’re all non-primes with the property that

\[2^{p-1}\equiv 1 \pmod p.\]

Now, all *primes* have this property: that’s what Fermat’s Little Theorem tells us (and an extension of this fact forms the basis of RSA public-key encryption, on which Internet commerce is based). But some exceptional composite numbers also have it, including those above. That prompts the following conjecture:

**If $n$ is merely poetic (or sheerly poetic) then $2\,n+1$ is either a prime or a pseudoprime to base $2$.**

I think I’ve proved that, and if you want to check whether you agree that I have (and I’d love you to), please contact me. But alas, the dance continues; yet again, the converse is false. There are pseudoprimes to base $2$ for which the corresponding value of $n$ isn’t merely poetic at all. One example is $645$: although it’s certainly true that $2^{644} \equiv 1 \pmod{645}$, the corresponding permutation, $\delta_{322}$, doesn’t have an order that divides $322$. (Its order is in fact $28$, which goes $11.5$ times into $322$.)

However, you’ll notice it does have an order that divides $2\times322=644$. That prompts another conjecture. Let’s call $n$ **nearly poetic** if ${\delta_n}^{2\,n}$ is the identity (so while you might not be able to finish your $n$-tina at the *end* of a cycle, you’d at least know you can finish it exactly halfway through one). Then

**If $2\,n+1$ is either a prime or a pseudoprime to base $2$, then $n$ is (at least) nearly poetic.**

Again, this is something I think I’ve proved. And this time, I’m pretty convinced that the converse is true: that if $n$ is at least nearly poetic, then $2\,n+1$ is either a prime or a pseudoprime to base $2$. However, I haven’t yet been able to prove the converse; if you can, I’d love to hear from you.

If you want to read further on sestinas and Queneau numbers, here’s a brief bibliography. Some of the key articles are in French, and don’t seem to have been translated, but the English paper by Saclolo is an excellent overview. If you do feel like diving into one of the French ones, I’d start with the Bringer paper.

Audin, M., ‘Mathématiques et littérature‘, *Mathématiques et sciences humaines***,** **178** (2007), pp 63-86

Bringer, M., ‘Sur un problème de R. Queneau‘, *Mathématiques et sciences humaines***,** **27** (1969), pp 13-20

Dumas, J.-G., ‘Caractérisation des quenines et leur représentation spirale‘, *Mathématiques et sciences humaines , *

Queneau, R., ‘Note complémentaire sur la sextine’, *Subsidia Pataphysica* **1** (1963), 79-80

Roubaud, J., ‘Un problème combinatoire posé par la poésie lyrique des troubadours‘, *Mathématiques et sciences humaines , *

Saclolo, M. P., 2011, ‘How a Medieval Troubadour Became a Mathematical Figure‘, *Notices of the American Mathematical Society*, **58(5)** (2011), pp 683-687

I’m involved with three sessions – a fun Maths Jam, a ‘how I used history in my teaching’ workshop and a research talk based on half my PhD. Here are the details:

**Monday 14th April 2014**

*A Taste of Maths Jam *- with Katie Steckles and some other MathsJammers.

19:30 – we’re one of the after-dinner entertainment options!

Maths Jam is a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting. Attendees range from hobbyists to researchers, with every type of mathematician and maths enthusiast in between. Events happen simultaneously in over thirty locations worldwide (mostly in the UK) listed on the website at www.mathsjam.com. Come to this event to get a taste of what happens at a typical Maths Jam night.

**Wednesday 16th April 2014**

*The unplanned impact of mathematics and how research is funded: a discussion-led activity*

Session F6 – 09:05-10:05

Mathematics is sometimes developed (or discovered) by a mathematician following curiosity with no thought of application. Later, perhaps decades or centuries later, this mathematics fits some application area perfectly. This aspect of mathematics has serious implications as increasingly researchers are asked to predict the impact of their research before it is funded and research quality is measured partly by its short term impact. A session on this has been used successfully in a UK undergraduate mathematics module on how maths interacts with wider society. This explored the concept of ‘unplanned impact’ and views on the phenomenon, as well as its impact on the way research is funded. This workshop will describe the session and demonstrate some of the activities used.

This session is one of a series on the History of Mathematics in Education coordinated by BSHM.

*Development and evaluation of a partially-automated approach to the assessment of undergraduate mathematics*

Session RI15 – 16:15-17:45

This research explored assessment and e-assessment in undergraduate mathematics and proposed a novel, partially-automated approach, in which assessment is set via computer but completed and marked offline.This potentially offers: reduced efficiency of marking but increased validity compared with examination, via deeper and more open-ended questions; increased reliability compared with coursework, by reduction of plagiarism through individualised questions; increased efficiency for setting questions compared with e-assessment, as there is no need to second-guess the limitations of user input and automated marking. Implementation was in a final year module intended to develop students’ graduate skills, including group work and real-world problem-solving. Individual work alongside a group project aimed to assess individual contribution to learning outcomes. The deeper, open-ended nature of the task did not suit timed examination conditions or automated marking, but the similarity of the individual and group tasks meant the risk of plagiarism was high. Evaluation took three forms: a second-marker experiment, to test reliability and assess validity; student feedback, to examine student views particularly about plagiarism and individualised assessment; and, comparison of marks, to investigate plagiarism. This paper will discuss the development and evaluation of this assessment approach in an undergraduate mathematics context.

**Edit 24/04/2014**: My paper in the proceedings is now available online:

Rowlett, P., 2014. Development and evaluation of a partially-automated approach to the assessment of undergraduate mathematics. *In*: S. Pope (ed.). *Proceedings of the 8th British Congress of Mathematics Education.* pp. 295-302. Available via: bsrlm.org.uk/IPs/ip34-2/BSRLM-IP-34-2-38.pdf.

Nathan says:

I see this as a great resource for researchers, research staff, academics and those who support researcher training. On the run up to my viva I had great advice from my supervisor, but I didn’t know about other resources that might help me prepare. The Viva Survivors Podcast will provide listeners with stories from people who have been through the viva, and give some insight on what to expect, what to do to prepare, and where to turn for help.

On the run up to my viva, I listened to a lot of the back catalogue and read Nathan’s e-book ‘Fail Your Viva: Twelve Steps To Failing Your PhD (And Fifty-Eight Tips For Passing)‘. Having used this in my preparation, I volunteered to be interviewed (you can offer to be interviewed too). The description for my episode says:

In this episode I’m talking to Dr Peter Rowlett, who recently completed his PhD at Nottingham Trent University. Peter’s research was multidisciplinary and was in the areas of computing and maths education; he did his PhD part time as well, and so we had a lot to talk about for this episode!

Viva Survivors Episode 23: Dr Peter Rowlett. Or subscribe.

Drinking game idea: take a drink every time I say “viva” when I clearly mean ‘thesis’.

Aside: Nathan is conducting a survey of PhD graduates of UK institutions since 2000. He explains why in a blog post. Consider filling it in.

]]>Number of dogs in the USA on anti-depressants = 2,800,000 https://t.co/FQkQBG8Cbg

— Mark Miodownik (@markmiodownik) April 4, 2014

A freshly-launched repository for curious, random factoids about numbers: https://t.co/CMj6M3ANLE Browse, and submit your own…

— Alex Bellos (@alexbellos) April 5, 2014

Fans of numbers will be pleased to hear that they now have their own social network. I’m not sure if I mean than numbers do, or fans of numbers do, but either way Meterfy is a newly launched internet website on which you can share, and discover, a huge quantity of numbers – statistics, constants, totals, averages and molar masses abound.

It has the potential to be a superb resource for numerical facts, although I did find a couple of nonsensical and demonstrably wrong entries, as well as some clearly jokey ones. All entries seem to link to some form of reference, such as Wikipedia, or a news article, so if you do pick a fact out for use elsewhere you can also get a source confirming it (a couple of those links are missing “http://”, and point to the wrong place – it looks like the input field for reference URL will accept anything, including ‘wikipedia’, as a value). *EDIT: Pete, who runs the site, has been in touch to say he’s fixed the URLs issue.* Some entries also lack context or scope (“18% of people leave work after 7pm” doesn’t mean much unless you know who was asked, and in how much of the world).

I’m not quite confident how would be best to browse the site – if you have a specific thing you’re looking for, they seem to make great use of keywords and hashtags to label topics, but it’d be good to have a ‘most shared’ or somehow rank them by interestingness, for the purposes of browsing aimlessly. The main page seems to list them by ‘most recently added’.

You have to log into the site to add your own numbers, and once you’re a signed up member you can ‘follow’ other users and ‘favourite’ entries, much like on Twitter. It’s easy to share entries to other social networks, and each entry can have its number edited or updated as time-stamped versions, which are all stored together.

See what you think – is this the new Twitter? Number Twitter? Two-itter?

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

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The video was made by amazing science TV guy Jonathan Sanderson, of StoryCog and ScienceDemo.org, who also helped to build the computer on the day (I have it on good authority that he personally placed ‘at least one domino’).

Since Matt likes to do things in prime-numbered multiples, this isn’t the only thing related to the Domino Computer you can watch on the internet. There’s also a Numberphile video, which is being posted today, in which Matt talks about the project:

And since Matt doesn’t really believe 2 is a proper prime number, he’s also posting a set of worksheets on his website at Think Maths, so you too can have a go at building logic gates from dominoes, and if you’re feeling ambitious, a domino computer of your very own. They’re designed for teachers so you can work with a class, but they’d also be suitable for bored people with too many dominoes (ooh me, me).

]]>*You may remember that we previously posted about Tydlig, a new calculator app for iOS. We asked if anyone would be interested in writing a review, and Aoife, who’s written the article below, kindly obliged.*

Tydlig is a reimagined calculator on iOS and provides an innovative, freeform canvas where multiple calculations can be built and organised in one space. It functions as a scientific calculator, but on an open workspace that you can control, with additional visual features. Elegant in its simplicity, Tydlig captures all of the necessary components of a calculator, while maintaining refined and intelligible functionality.

And the tutorials are just as sleek. Not that you need them; it doesn’t take much playing around to get the basics. Start typing and you can put numbers and operators into an equation and the result is calculated for you at the touch of the equals sign. Equations can be freely moved around on your own canvas, and edited by simply touching the component you want to change. If you press and hold, you get a menu that leads you to options like graphing your equation or linking your number to use in another equation.

For learning, this kind of visual representation of one’s own positioning of calculations and their graphs can be very valuable. Watching results update as a result of your actions is a powerful learning tool, and while some calculators make trial and error cumbersome, Tydlig’s responsive results are a joy for experimenting.

You can drag and drop variables into existing graphs, or create new blank ones. Editing graphs is as simple as editing an equation: just touch any number for options. There is a full set of traditional scientific operators to choose from as well as extra features that make computing intuitive, for example a percentage can be calculated as an addition: **“78+7%=”**. This may prove useful in day-to-day maths, and is easily accessed on a smartphone. For instance when handed the dinner bill and blindly trusted with mathematical wizardry, one can quickly demonstrate the effect of adding various tips, and the total for each person will update accordingly.

While extras like the “percentage” function could undoubtedly make everyday calculations more accessible, it may itch some mathematical sensibilities by inserting a symbol that traditionally doesn’t make sense in an addition, especially for those who have spent years teaching a percentage increase as a multiplication. But for general use over mathematical learning, there is a good argument for usability over rigour.

While Tydlig is concise and intuitive, as with any new interface, there are conventions to be learned. There is a notable lack of cursor, which means when you are typing *on* a number, you are actually typing to the *right* of that number. So it takes a few goes to shake the feeling that typing will replace the text of a highlighted number. Handily, mistakes are easily rectified with “undo” and “clear all” buttons, so mistyping has less of the annoyance of using a typical calculator. Admirable consideration has been given to the design, and as a result Tydlig is beautifully simple and refreshingly autonomous.

Even though it is not necessarily in a calculator’s remit, there is a glaring omission of algebra, particularly with the graphing function. It is perhaps only instinctive to some to want to plot $\sin x$, as opposed to $\sin 1$, and then adjust the variable. But it could also be argued that algebra is better instilled by introducing initial variables numerically as Tydlig requires. Either way, experimentation is key to making the best use of this app, and on an open canvas users are given the tools and creative license to make it fit for their own use.

Tydlig doesn’t have the range of mathematics functionality of, say, GeoGebra, but for non-mathematicians it is the user-friendly option. To the challenge of ergonomic design, and compared to clunky Casios, it lives up to its name: *tydlig* is Swedish for ‘clear’.

*Here’s the official trailer/advert for Tydlig, so you can see it in action:*

Download Tydlig on the App Store (£2.99/$4.99 at time of publication)

@tydligapp on Twitter

]]>I highly recommend Incredible Numbers, iPad app by Ian Stewart. New gold standard for interactive maths. For all. https://t.co/bI9YfUpViP

— Alex Bellos (@alexbellos) March 31, 2014

and how could we resist? We borrowed a nearby iPad, downloaded the app and had a play.

What struck us first was that the app is very much like reading a good popular maths book, except with interactive diagrams that you can fiddle about with and lots of pretty pictures. It’s all beautiful and well executed, and while the app gives you a path to follow whilst explaining things, and instructions on what to do, it doesn’t mind too much if you mess about a bit.

*Incredible Numbers* is divided into eight main areas, each of which covers a different topic in maths – mostly numbers, although some shapes do creep in, and infinity isn’t a number – and each has around three short articles, containing interactive sliders to punctuate the text, accompanied by one main interactive demonstration gadget, depending on the topic.

The app makes good use of the iPad control system, with lots of sliders and pinch-zoomable images, although some are a little difficult to control precisely - disappointingly, some zoomable diagrams which could have been generated on-the-fly and go on for much longer stop after a certain amount, which made us a bit sad, but they do go pretty far – there’s a million digits of π, which you can search for your birthday in: mine was in the 84,851st decimal place.

Our personal highlights included: a simplified enigma machine you can use to encode/decode text; a beautiful sunflower seed arranger allowing you to specify the angle, which shows off the Golden Ratio nicely; and an XKCD-esque noughts and crosses grid, explaining and demonstrating the 9! ways to order 9 things. The app also includes a selection of maths puzzles which kept us going for a while.

We did succeed in crashing the app while playing with the Hilbert’s Hotel animation; although admittedly we had countably infinitely many countably infinite sets to fit in, and I’m not sure how much RAM an iPad has. We did get it working again shortly afterwards, and then spent ages playing with the interactive ‘approximations to π’ sliders, to see whose approximation is the best (go Chudnovsky!).

There wasn’t much to see that hasn’t been done before elsewhere – I noticed a version of the Factor Conga, among other things – but everything that’s there is interesting, and the maths is well explained. This would make a great gift for someone you’d buy one of Ian Stewart’s books for, and would be great for inquisitive youngsters (actual age or mental age) who want to discover things for themselves, but whose attention spans are too short for the printed word.

One of the reviews on the app store complains that the explanations are pitched too high for a complete non-mathematician – which might be a fair accusation, as they do assume a little knowledge – but if you’ve got no maths background whatsoever, it’d be great working through it with someone who could explain things to you.

Download *Incredible Numbers* on the App Store (£2.99 at the moment)

*Incredible Numbers* official website

@incnumbers on Twitter

Ian Stewart on Twitter

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