# Book of the Year 2020

A few weeks ago, we announced the 7 book shortlist for the 2020 Chalkdust Book of the Year. In this post, we announce the winner of this award.

We will be awarding two prizes: the Chalkdust Book of the Year (as chosen by our editors), and the Chalkdust Readers’ Choice (as voted for by our readers).

## Chalkdust Book of the Year 2020

We found picking a winner of this award really difficult, as all the books on the shortlist were deserving of the prize (obviously, as if not they wouldn’t have made the shortlist). The one thing that set the winner apart from the other books was the innovative ways in which it got the reader to interact with it, and the way it could be enjoyed by older readers as well as children. And the winner is:

## Molly and the Mathematical Mystery

#### Eugenia Cheng and Aleksandra Artymowska

This book (Amazon UK, Waterstones) is an interactive children’s book that encourages the reader to solve clues to follow the adventure.

You can read our full review of Molly and the Mathematical Mystery here.

As well as picking our favourite from the shortlist, we held a vote for our readers to pick their favourite. The runaway winner of this poll was:

#### Ioanna Georgiou and Asuka Young

This book (Amazon UK, Waterstones, Tarquin) is a children’s book the takes the reader on a journey through the history of maths.

# The Wonder Book of Geometry

David Acheson is a mathematician at Jesus College, University of Oxfors. The Wonder Book of Geometry (Amazon UK, Waterstones, Oxford University Press) is a book that takes the reader on a journey through the world of geometry.

## Style

The Wonder Book of Geometry starts by recounting a story of a young David Acheson being surprised: he drew a semicircle, picked a point, then draw lines from the endpoints of the diameter to the point. He then measured the angle. To his surprise, the angle was always 90°, now matter where the point was placed. Mathematics is full of this type of surprise, and this book shares many situations with the reader. Many of them may be familiar to many readers, but you cannot fail to enjoy a nice surprise at a fair few of them.

## Control

After showing the 90° semicircle fact, The Wonder Book of Geometry looks at why it is true. This is another very satisfying bit of maths, as when viewed in the right way, the result goes from being surprising to being ‘obvious’. Rather than spoiling the result by taking away the mystery, seeing how it is true in this way actually makes is better. As David puts it: “this is often one of the hallmarks of mathematics at its best.”

## Damage

While the book starts with the kind of angles, areas, and shapes that will be familiar from secondary school (although going back and seeing why these results are true is always fun), it soon moves into less familiar territory, covering less well known results related to circles and triangles, as well as other topics such as sphere packing an non-Euclidean geometry.

## Aggression

I would recommend this book to anyone wanting to rekindle their love of geometry, or looking to revisit geometry and leave with a deeper understanding of why things are true.

Now that we’ve review all the book’s on this year’s shortlist, you can vote for your favourite. The book with the highest number of votes will be crowned the 2020 Readers’ Choice. Voting closes at 5pm on Saturday 13 March.

What is your favourite book on the 2020 Book of the Year shortlist?

• Mathematical Adventures! by Ioanna Georgiou and Asuka Young (63%, 1,181 Votes)
• Hello Numbers! What Can You Do? by Edmund Harriss, Houston Hughes and Brian Rea (34%, 639 Votes)
• Why Study Mathematics? by Vicky Neale (1%, 26 Votes)
• The Wonder Book of Geometry by David Acheson (1%, 10 Votes)
• Geometry Juniors by Ed Southall (1%, 10 Votes)
• Molly and the Mathematical Mystery by Eugenia Cheng and Aleksandra Artymowska (0%, 8 Votes)
• How to Make the World Add Up by Tim Harford (0%, 8 Votes)

Total Voters: 1,882

# Hello Numbers! What Can You Do?

Edmund Harriss is a mathematician, artist, and assistant professor at the University of Arkasas. Houston Hughes has produced hundreds of live shows in collaboration with musicians, chefs, scientists, mathematicians, and others. Brian Rea is an artist and painter from Los Angeles. Hello Numbers? What Cah You Do? (Amazon UK, Waterstones, Workman) is a children’s book about numbers.

## Style

Hello Numbers! takes the reader through the numbers from zero to five (inclusive) and encourages the reader to count, arrange a number of points into shapes, and look for ways to add to make numbers. The rhyming sentences on each page are accompanied by charming and colourful drawings that show some of the things that can be done with each number.

## Control

As well as encouraging the reader to count, this book suggesting thinking about some other properties of numbers: the three characters that make up the number 3 can be arranged into a triangle; four character can made a square, or other four sided shapes, or a pyramid; five characters can make a star. A real strength of this book is that it shows irregular shapes that can be made as well as equilateral triangles and squares. Perhaps my favourite page is the one with a triangle so long and thing that it stretches across the whole double page spread.

## Damage

This book is probably suitable for a younger audience than many of the other books on this year’s shortlist, as it encourages the reader to engage with more basic mathematical ideas than the others. This is no way a bad thing, as younger readers need reasons to love maths as well as older reasons.

## Aggression

I’d recommend this book to anyone with younger primary aged children or relatives looking for a fun book to encourage some number-related exploration and play with a child. I’m looking forward to seeing what my niece thinks of it on her birthday later this year…

# Why Study Mathematics?

Vicky Neale is a mathematics lecturer at the University of Oxford. Why Study Mathematics? (Amazon UK, Waterstones, London Publishing Partnership) is book that looks into studying mathematics at university.

## Style

Why Study Mathematics? is a book aimed at 16-18 year-olds considering studying maths or related subjects at university. The book is split into two parts. The first part discusses what is involved in the study of university mathematics, why you should consider studying maths, and what people go on to do after a maths degree. The second part looks at a few university-level mathematical topics.

## Control

This book gives a very informative view into what studying maths is like, and a very readable introduction to the mathematical topics it covers in the second half.

## Damage

This book is a must-have for every school library, as it will be an invaluable source of information for any students considering a mathematical degree.

## Aggression

If you already have a maths degree (especially if you got it reasonably recently), this book isn’t for you. But if you don’t have one and are considering studying for one, I could not recommend this book more highly. I really wish this book has been written a while ago, so I could’ve had it when I was 17 and looking at universities.

# Molly and the Mathematical Mystery

Eugenia Cheng is a mathematician, author, baker, and concert pianist (you can find out more about her by reading our interview with her from issue 09). Aleksandra Artymowska is an author and illustrator of children’s books. Molly and the Mathematical Mystery (Amazon UK, Waterstones) is an interactive children’s book that encourages the reader to solve clues to follow the adventure.

## Style

Molly and the Mathematical Mystery is a beautiful book. Its pages are large, and full of wonderful illustrations. On each page, the reader is encouraged to help Molly continue on her adventure by finding information under flaps, opening flaps to change available routes, or even using the flaps to construct a path for Molly that takes her out of the page.

## Control

Molly’s adventure leads the reader through a range of mathematical ideas, including fractals, symmetry, and Latin squares. The reader is encouraged to interact with the book to experiment with these ideas, then more information about each one is given at the end of the book.

## Damage

The use of flaps that can be lifted, moved, and rearranged really sets this apart from other children’s maths books. I was particularly impressed with the page on which I had to attached the flaps together to make cubes that Molly could walk around to find her path to the next page.

## Aggression

I’d recommend this book to anyone with a child or young relative. There’s lots to enjoy in this book for children of any age: younger children can interact with the book by lifting the flaps to look for clues, while older readers could engage with the mathematical ideas and puzzles spread throughout the book.

# How to Make the World Add Up

Tim Harford is an economics and journalist, and the presenter of More or Less and How to Vaccinate the World on BBC Radio 4. His latest book, How to Make the World Add Up (Amazon UK, Waterstones, Maths Gear (signed)), is a book about making sense of statistical claims about the world around us.

## Style

Fans of Tim Harford will be unsurprised to find that How to Make the World Add Up is an enjoyable read: it has the same informative and entertaining tone as his other books and programmes.

## Control

How to Make the World Add Up puts its points across very clearly, and the ideas contained in each chapter are made more concrete through anecdotes about situations where the topic of the chapter was relevant.

## Damage

Statistics are often misused. As the introduction of this book points out, there is a danger that this can lead to a general distrust of numbers in the news. In the current times, however, it is increasingly important that we can trust statistical claims about virus spread and vaccines, while being distrustful of incorrect claims. This books aims to show the reader ways in which they can work out what to trust, while remaining sceptical when claims are too-good-to-be-true (or too-bad-to-be-true). In a world where mathematical and statistical claims are so much more visible than we are used to, this is a particularly important book.

## Aggression

I would very strongly recommend this book to fans of More or Less, as if you enjoy it then you’ll certainly be a enjoy this book. If you’re not a fan of More or Less, then reading this book might lead you to becoming a fan of More or Less.

# Geometry Juniors

Ed Southall is a teacher and geometry puzzle fan. His latest book, Geometry Juniors (Amazon UK, Waterstones, the Mathematical Association), is a book of prompts and puzzles aimed at a young reader.

## Style

Geometry Juniors contains a large collection of geometry prompts to encourage discussions and problem solving. Each prompt features a picture of a geometry situation, some questions you might pose about the situation, and some delightful illustrations (by Nicole Lane). The introduction of the book suggests these could be used to start conversations between a child and a parent or teacher.

## Control

People who follow Ed on Twitter or have worked though his Geometry Snacks books (co-authored with Vincent Pantaloni) will know that Ed has great taste in geometry puzzles. This shines through in this book, with some really great situations to get you thinking. Many of the prompts have been carefully selected to catch some common misconceptions, and to lead the reader to question these. I’m a particular fan of the coordinates section, in which many of the prompts suggest adding a point to make a certain shape before suggesting that there may actually be multiple different points that could’ve been added.

## Damage

This is a very good book for anyone looking for mathematical tasks to do with a child, and the tasks have obviously been very carefully designed to promote deep mathematical thinking. Many of the tasks lead to open ended exploration, and encourage the reader to keep asking “what if”. It’s the kind of book that I wouldn’t be surprised to find a future mathematician citing as the book that made them fall in love with maths.

## Aggression

I’d highly recommend this book to teachers or parents looking to engage someone in mathematical conversations and to encourage mathematical thinking and problem solving.

Ioanna Georgiou is a mathematics teacher from London and Asuka Young is a freelance graphic designer and illustrator. Their book, Mathematical Adventures! (Amazon UK, Waterstones, Tarquin), is a children’s book the takes the reader on a journey through the history of maths.

## Style

Mathematical Adventures! takes the reader through the development of maths in a series of colourful and well illustrated pages. It covers the development of numbers and algebra and some famous historical maths problems, before catching up with more recent maths such as differently sized infinities and Cantor’s diagonal argument. It encourages the reader to stop and think about problems themselves throughout the book.

## Control

The book contains very clear and readable explanations that would be very suitable for a parent reading with a child.

## Damage

This book doesn’t shy away from difficult ideas, such as the existence of different sizes of infinity, and offers an excellent opportunity for a child to meet interesting bits of maths that would often be deemed “too difficult” for a few more years. An adult reader who is keen on maths (the kind of person who is likely to be reading Chalkdust!) will probably be familiar with the majority of the ideas in this book, but it would be a great way to rediscover and share these ideas with a younger relative.

## Aggression

I’d highly recommend this book to anyone looking for something to read with a younger relative. I’ll be saving my copy for a few years until me niece is old enough to read it with me.

# 7 ways to tell if a number is divisible by 7

I’m sure you know how to check if a huge number is divisible by 3, 9, 11 or by powers of 2 like 2, 4, and 8; you were probably taught how to do this in primary school. However most of you were probably never taught how to test whether a number is divisible by 7. In this article we will explore seven different ways to do that.

7 is by far the least-loved single digit number when it comes to divisibility. Image: Chalkdust

Before we start, let’s introduce some notation which we’ll use throughout the article. An $n$-digit number $N$ in decimal base 10 is a number with digits belonging to the set $C_{10}=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$ and can be expressed as sum of powers of 10: $N=\sum_{i=0}^{n-1}10^ic_i,$ where  $c_i \in C_{10}$. We normally write this number by concatenating the digits using their position to indicate the corresponding power of 10: $c_{n-1}c_{n-2}\cdots c_1c_0$. The least significant digit of $N$ is $c_0$, and most significant digit is $c_{n-1}$. Continue reading