Welcome to the 89th Carnival of Mathematics, this month hosted here at The Aperiodical. While The Aperiodical team is involved in administrating the Carnival (more information about the Carnival can be found here), it is hosted on a different blog each month. Last month cp’s mathem-o-blog was the host for Carnival of Mathematics 88, and next month the Carnival will be hosted by Mike Croucher at Walking Randomly.

In the Carnival of Mathematics tradition, I feel it is my duty to point out that 89 is both a prime and a Fibonacci number (and in fact, its reciprocal $\frac{1}{89} = 0.011235955\ldots$ excitingly has the first few Fibonacci numbers at the start of its decimal expansion). It’s also the number of square pieces you’d need to construct one of each $n$-omino from $n=1$ to $5$ (as Wikipedia points out, this is precisely the set of pieces each player is given in a game of Blokus.)

This Carnival features posts from a whole range of blogs, some of which have been contributed and others I’ve found myself during my regular internet browsing. I’ve made no attempt to order or categorise them, but have weaved an epic narrative with beautiful topic segues that would make a One Show presenter get a little bit misty-eyed.

Andrew Taylor, sometime Aperiodical contributor, has written this blog post about different keyboard layouts and which are most prone to typing errors. The post comes complete with a lovely statistical analysis, with graphs, of which keyboard layouts would lead to more typing errors on adjacent keys, as well as an optimal keyboard layout (and hilariously, a least efficient layout). It’s also sparked off quite a discussion about nerdy alternative keyboard layouts in the comments.

Andrew has also written this lovely piece about the use of comparative quantities in describing scientific discoveries, or what he calls ‘journalist units’. He decides on standard units and gives some handy conversion charts (otherwise, your working-out might take up an area the size of Wales).

Another post from Andrew about URL shortening linked to this blog post from 2010 about memorising number strings, which gives a nice method involving associating each digit with a person, object and verb and imagining that person doing that verb to that object in a location on a memory path (e.g. through your house). If you manage to use it to memorise any serious number of digits, please let me know.

Speaking of arbitrarily long strings of digits, this post on Math Frolic entitled Another Prime Example gives a simple way of creating arbitrarily long sequences of consecutive integers that include no prime numbers. Before you read it, see if you can think of a way! Then see if the way you thought of was the same way.

The above could easily have been discussed at one of the monthly Maths Jam evenings – it’s exactly the kind of thing that gets talked about there. Speaking of which, this blog post at Matheminutes details a way of playing 4D noughts and crosses using the cards from the game SET. If that isn’t Maths Jam material, I don’t know what is.

Math Goes Pop (a blog digging into the mathematics behind TV programmes, movies and other aspects of pop culture) has posted this piece about reality show The Friend Zone, the premise of which is explained in the blog post but hinges around people who are secretly in love with their friends, and discusses the probability of making it out of ‘the friend zone’ on the occasion of a confession. Mathematicians will be relieved to learn that, should they ever succeed in making any friends, the stats are reassuringly good.

Math Goes Pop has also posted a couple of nice pieces under the banner of Hot Dog Mathematics part 1 and Hot Dog Mathematics part 2 in which, almost perfectly timed for the spate of BBQ-friendly weather we’ve been having, the surface-area-to-volume ratio of various Hot Dog preparation methods is discussed. The first part deals with different ways of slicing (and also mentions the All Edges Brownie Pan, which is superb), while the second part considers the sausage phenomenon that’s been sweeping the internet – spiral cut Hot Dogs, and the effect such flamboyant slicing has on surface area and hence deliciousness.

Mike Thayer submitted his post Zen and Fermat’s Last Theorem, a philosophical discussion about the nature of learning, saying: “I’ve been thinking a lot lately about how I try to teach math, and I had a revelation of sorts about why I do (some) things the way I do. In my post, I try to describe where this realization came from, and what it means for my teaching in the future. I think it might resonate with others.” Does it resonate with you?

In recent news, there’s been all that Higgs stuff. In this blog post (the fourth in a series of four), The Unapologetic Mathematician explains a little of what the Higgs field is and how it does its thing. Also, here, Doc Madhattan explains it from a physicist’s viewpoint. So now you can stop pretending to everyone else you know what it’s all about, and actually have some idea. Similarly, Evelyn has written Five Sigma–What’s That? just in case you weren’t sure (it was the p-value for the Higgs discovery). While we’re on the subject, Peter Rowlett collates a selection of tweets on the topic of Duck Physics – not the calculation of the precise moment to move out of the way of an approaching projectile, but an emerging field based on the observation that the Higgs Boson ‘quacks like a duck’. Apparently.

Alexandre Borovik’s Micromath blog is often a source of interesting nuggets, and this month he’s posted this follow-up piece to a previous post he wrote in 2006 about the aggressive nature of mathematical research, and some thoughts he’s been sent by others (female and male) about how some women find it intimidating, which might go some way to explain the disparity in gender within research mathematics.

Greg Ross’s Futility Closet, a blog which seems to alternate between posting curiosities, chess problems, and nice little maths puzzles, has put a few nice ones up this month, including but not limited to: a nice puzzle about distance sums; knot theory meets probability; everybody loves triangles; a puzzle about tape reels; a neat fact about calendars; the Gilbreath principle in card shuffling; a nice puzzle with a water tank; and Sicherman dice.

Mr Gregg has written this piece called The Human Calculator, about how, sick of hearing them whinge about not being allowed to use a calculator, he decided to see how his students would like it if they were themselves the calculator, and his experiences of creating a binary calculator out of pupils. I guess it’s one use for them.

This post from Kevin Kelly’s blog (and apparently an article in Wired) give high praise to Dragon Box, a maths teaching app (one of approximately four billion available for iPad) which allows you to treat items in a formula like boxes, and ‘kill’ the ones on each side, giving an intuitive explanation for cancelling in algebra. Do you know any good maths apps? What about for more advanced maths?

Pi approximation day (22/7) was this month – a much more British (date format) version of Pi day, and in honour of it, Evelyn Lamb of Scientific American has written a piece entitled How Much Pi Do You Need? which discusses how many digits of pi are needed for different levels of accuracy and different applications, compared to how many are known. She’s also written this explanation of a classic ‘prisoners and boxes’ puzzle, inspired by attending this event at the surely-to-be-open-any-day-now Museum of Math in New York.

There have also been loads of great things posted here at The Aperiodical, both by the editors (such as this video by me and Christian Perfect about our fun using paper enigma machines), and our contributors (such as this piece by Paul Taylor about language used to describe relative quantities of things, and how he finds certain phrases ten times more annoying than others). For more stuff from The Aperiodical, feel free to browse the site or check out our irregular round-up podcast, the Aperiodcast, where we discuss what the week’s hot stories are and what to look forward to.

Next month’s Carnival will be hosted by Mike Croucher at his blog Walking Randomly, which this month includes posts about Olympic themed computer games, MATLAB, Graphene and loads more, and is well worth a look. Watch out for the announcement of the next Carnival of Mathematics both here on The Aperiodical, and on the Twitter feed at @carnivalofmath.