Carnival of Mathematics #118

June 2015

Hello! It’s been about a month since the last Carnival of Mathematics, and therefore high time we did another. We’ve done 117 before, which means (a) that this is number 118, and (b) that there are only another infinity to go before we have to think of a new numbering system for them.

Tradition dictates we open with some interesting fact about the number 118, preferably a fact that does not involve directory enquiry services. Wikipedia offers the rather pleasing fact that:

• 14 + 50 + 54 = 118 and 14 × 50 × 54 = 37800
• 15 + 40 + 63 = 118 and 15 × 40 × 63 = 37800
• 18 + 30 + 70 = 118 and 18 × 30 × 70 = 37800
• 21 + 25 + 72 = 118 and 21 × 25 × 72 = 37800

It says “there are no smaller integers that can be expressed as the sum of three integers such that each set of three has the same product” but that doesn’t quite make any sense. Let’s just enjoy the nice maths above and hope we’ve figured out what it all means before Carnival 37800 rolls around in March 5155.

Fortunately, I’ve been sent many better written and broadly coherent mathematical blog posts in the last month, so here is an unordered subset of them, including not-strictly-fewer-than two non-Euclidean songs.

Let’s start with Joey Devilla’s post about the New York Times vs algebra, because the whole story amuses me greatly.

Alex Bellos has written about Conway’s Game of Life including some lovely videos showing some advanced things you can do in it. If you want to play with Conway’s Game of Life, Alex Bellos’ blog has links to Golly, which he used to make the videos, or you can have a quick play in your browser with this version that I made — with source code on Github.

You can use it to build computers. If you are wondering whether Game of Life can therefore answer all mathematical problems, then you should read Haggis the Sheep’s blog, which uses The Imitation Game as a starting point for discussing maths Alan Turing worked on.

Speaking of Turing, this blog discussed whether Newton might also have been gay, and whether it matters. I think the take-home message to any gay mathematicians out there is stay the hell away from apples.

There’s more open-source 2D maths simulation at Simon Gladman’s blog, where he has made an iPad app that lets you tinker with diffusion, and a nice bit of Javascript demo’d geometry courtesy of Joshua Fisher.

Meanwhile Vi Hart and friends have been busy open-sourcing some mathsy art brought to you by winter and the number twelve, including a mildly terrifying stroll through a hyperbolic Christmas song.

David Mumford has written an obituary for Alexander Grothendieck. I don’t really understand much of the maths in there, though, but apparently neither does Richard Elwes who has written a song to that effect. I’ve just linked to it. I am not even the best at not understanding this.

Evelyn Lamb sent a link to her student’s blog, who had made a pseudosphere out of wood by rotating a tractrix about its asymptote, because geometry has the coolest words. If you prefer your mathematical furnishings soft, there’s a poll on Spoonflower looking for the best mathematically themed fabric. There are some pretty nice ones if you click through to the full list.

William Wu has had a busy month — as well as blogging about how unlikely it is that the three recently-missing fight numbers add up to 8888 and the Dragon Curve, he’s branched out into videos. His first is a three-minute video about factorising the difference of two cubes, which shows a couple of nice moves that seem obvious in hindisght but I don’t think I’d seen before. He has a second video proving that root 2 is irrational, which is longer than the first but at least correct, unlike this proof that 2 = 1, which Colin found on Futility Closet — a reliable source of interesting stuff and the occasional infuriating nonsense with no comment box — and interestingly dismantles for us on his blog.

John Cook has (for some reason) been counting primitive bit strings which gets very mathsy very fast — if anyone has a link to a blog post about how on Earth the Möbius function manages this neat trick then I’ll add it in here.

Showbiz news now, and Slate have an interesting article about the “mathematical Oscars” given out recently, and Chris Burks has a post about a recent maths category in the childrens’ version of Jeopardy. I invite you to ponder the absurdity of any forwards quiz show posing the question “what is three”, much less expecting the bafflingly unhelpful answer “1 - 2 + 3 - 4 + 5”.

That’s nearly the end of the Carnival for this month, but if you want more link-heavy mathsy roundup, Frederick Koh has submitted his 2014 roundup.

I thought this was going to be a roundup of 2014 as well, but it turned out to be instructions for making a gingerbread dodecahedron, so go and do that.