## Carnival of Mathematics #113

Welcome to the rather delayed Carnival of Mathematics for July. This is the 113th edition of the mathematical blogging tradition that’s organised by Katie and company over at The Aperiodical.

**Number Trivia and a challenge**

Long held tradition dictates that I find something interesting about this month’s edition number – 113 – and I turn to Number Gossip for help. It comes up with 3 very nice little prime tidbits:

- 113 is the smallest three-digit permutable prime
- 113 is the smallest three-digit Unholey prime: such primes do not have holes in their digits
- 113 is the smallest three-digit prime whose product and sum of digits is prime

**Walking Randomly Challenge**: Prove the above using the programming language of your choice and post in the comments section. Here’s a demonstration of the first statement using Mathematica.

(*Returns true if num is a permutable prime*) permutePrimeQ[num_] := AllTrue[PrimeQ[Map[FromDigits, Permutations[IntegerDigits[num]]]], TrueQ] (*prints all permutable primes from 1 to 1000*) Do[ If[permutePrimeQ[x], Print[x]] , {x, 1, 1000} ] 2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 199 311 337 373 733 919 991

**On with the show**

**Mathematical software blogs**

A math carnival wouldn’t be a WalkingRandomly math carnival without some focus on mathematical software blogs. Loren of The Art of MATLAB brings us Analyzing Fitness Data from Wearable Devices in MATLAB which is a guest post by Toshi Takeuchi. The new computational programming language on the block is Julia and the Julia blog contains videos and code on mathematical Optimization in Julia. The Wolfram Blog has a video on how to Create Escher-Inspired art with Mathematica (Don’t forget that Mathematica can be had for free for the Raspberry Pi).

Sage is a free, open-source alternative to Mathematica, Maple and MATLAB and the SageMath blog recently published SageMathCloud — history and status. The Numerical Algorithms Blog, on the other hand, brings us Testing Matrix Functions Using Identities. Efficient linear algebra routines form one of the cornerstones of modern scientific computing and July saw the publication of a tutorial on how to write your own, super-fast Matrix-Matrix Multiply routine.

**Stamps, Making Change and Dealing Cards**

When was the last time you used a postage stamp? Even if it was a long time ago, you may have held in your hands a strip of stamps. Maybe you have even tried to fold it into a stack, one stamp wide, so that the strip was easier to store. Have you ever wondered how many ways there are to do so? This post reviews a recent research survey about the topic.

How many ways can you make change for a dollar? This post gives a Lisp program that solves the problem and an analytical solution based on generating functions.

Over at The Aperiodical, home of the math carnival, Dave Wilding has been Discovering Integer Sequences by dealing cards.

**Ninjas, Lord Voldemort and Hairy Hay Balls**

Colin Beveridge has written a delightful follow-up to Pat Ballew’s post which featured in CoM112 – Trigonometric Trick Secrets of the Mathematica Ninja.

Ben of Math with Bad Drawings fame has written a highly readable rant about a bit of syllabus design which will resonate with anyone teaching (or learning) mathematics in The Voldemort of Calculus Classes.

New math blogger, Grace, recently had an experience in which her math education intersected with her everyday life in Hay Ball Meets the Hairy Ball Theorem.

**Tweeting bots, 3D Printed Geometry and Hair ties**

*(/begin shameless plug)* I spend a lot of time on twitter posting as @walkingrandomly *(/end shameless plug)* and have discovered quite a few mathematical twitter bots in my time. Evelyn Lamb has discovered many many more and has posted reviews of them all over at Roots of Unity.

James Tanton posts fun problems on twitter all the time. One particular problem caught the attention of Mike Lawler because of how 3D printing could help younger children see the geometry.

If you’ve ever wondered what a 120-cell would look like if it were made out of hair ties, wonder no longer because Andrea Hawksley has made one – Hair Tie 120-Cell (By the way, hold your mouse of the title of her blog – it’s cool!)

**More Ninjas, Dots and Mandelbrots**.

A round-up of fun stuff from Colin Beveridge’s “Flying Colours Maths” – a kind of @icecolbeveridge carnival for Mathematics Carnival.

Have you ever wondered what mathematics is behind those pretty Mandelbrot posters that are all over the place? Find out over at Grey Matters: Blog – Mandelbrot Set: What Exactly Are We Looking At, Anyway?

Did you know that dots have power? To see how much power, check out Keith Devlin’s article The Power of Dots.

**Football, drugs and underwear**

Since I’m not a big fan of football at the best of times, the football world cup is a distant memory for me (England’s dismal performance didn’t help much either). Fortunately, there’s more than one way to enjoy a world cup and Maxwell’s Demon and The Guardian helped me enjoy it in a data science way: How shocking was Brazil’s 7-1 defeat, mathematically speaking? and Data Visualization, From The World Cup To Drugs In Arkansas.

At this time of year, many of us turn our thoughts to vacations. If you are a math geek, you owe it to yourself to optimise your underwear and pack like a nerd.

**Puzzles, Games and playing like a mathmo**

When I’m on vacation, I often take a notebook with me so I can do a little mathematics during downtime. My wife and friends find this extremely odd behaviour because mathematics looks like hard work to them..in short, they don’t know how to play like a mathematician.

My job at The University of Manchester is wonderful because it often feels like I am being paid to solve puzzles. While on vacation, however, I have to find some unpaid puzzles to solve and this concentric circles puzzle is an example of one thats fun to solve.

I think that one of the best ways to learn is through play and games and, in a new post over at Math Frolic, a Li’l Game From Martin Gardner introduces mathematical “isomorphism.”

**Cartoons and Limits**

Mathematics is everywhere, it’s even in the voice bubbles used in web comics! As an added bonus, this blog post contains a little Python programming too.

Next up, we have Part 2 of Bressoud’s masterful investigation (Part I featured in Carnival 112) of how students understand limits.

**Resources, Exams and Books**

Colleen Young brings us a great set of Standard Form Resources.

Patrick Honner continues his long-running evaluation of New York State math Regents exams, the high school required exams there. In this post, he looks at a multiple choice question that asks the student to identify the graph of an “absolute value equation”.

The Maths Book Club gives details of their most anticipated maths books for the rest of 2014.

**Bad Mnemonics and a Dislike of Mathematics **

Andrea Hawklsey muses on why some people dislike mathematics when they have interests that suggest they should. Perhaps it has something to do with poorly executed mnemonics when students are taught mathematics, or perhaps its just because they had dull math teachers? Most of my math teachers were awesome and I’ve always felt that this was a major factor in me enjoying the subject.

**Skirts, Snow globes and Mathematical Mind Hacking **

This edition of the carnival is in danger of becoming the Carnival of Andrea Hawksley since so many of her great posts were submitted! In one of her July posts, she manages to combine fashion and hyperbolic geometry – which is quite a feat!

The author of cavmaths has been musing over the dynamics governing snow globes. Can anyone help out?

Hacking your mind sounds like it might be dangerous but it turns out that it’s really quite safe. Head over to Moebius Noodles to see an example of a mathematical mind hack.

**That’s all folks**

Thanks to Katie for inviting me to host this month’s carnival, thanks to everyone for submitting so many great articles and thanks to you for reading. Carnival #114 will be hosted over at SquareCirclez.

I think that the idea behind the new Mathematica function is that you use it like this

AllTrue[Map[FromDigits, Permutations[IntegerDigits[113]]], PrimeQ]

or you could simply write

And @@ PrimeQ[Map[FromDigits, Permutations[IntegerDigits[113]]]]

Those problems are easier to solve mentally than program.

1. 113 is a 3-digit permutable prime. Any prime with a zero has a permutation that ends with zero, so is not prime. 111 is not a prime.

2. 113 is a unholey (unmoley) prime. Zero has a hole, so such a prime cannot have a zero.

3. For a prime to have its product be a prime, one of its digits must be a prime and all the other digits must be one.

Q.E.D.

I see your point, thanks for that. It seems that the first thing I think when I see a problem these days is ‘How can I solve that with a computer?’

@Juan, Yes – your usage does look nicer