Flo-maps fractograms: the game

This game corresponds to the article Flo-maps fractograms: the prequel. Have a go!


Here, you provide a numerator and denominator to receive a beautifully graphed pattern depending on the resultant decimal.

You must also designate the number of decimal places you wish to show: please do not use a number greater than 500.

Similarly, please try to keep the number of decimals a multiple of 100 for numbers larger than 100, and a multiple of 10 otherwise. This is not mandatory, however may result in visual bugs if not followed.

The recommended numbers of decimal places are: 10, 50, 100, 200, 500.

Please keep the denominator larger than the numerator, as the program will only illustrate decimal place patterns.

Once you have chosen your numerator, denominator, and number of decimal places, just press “Go”.

The “Superimpose” option will allow you to superimpose different patterns on top of each other. Please only use it after you have already shown one pattern.

Have a go


Flo-maps fractograms: the prequel

My original interest in decimal fractions was due to studying the ‘chaotic dropper’ experiment (see Fractograms from Chalkdust issue 02). Long before this, I had read about modelling the growth of a population and finding that it, too, can demonstrate chaotic behaviour. This is shown by using a logistic map. I realised the digits of decimal fractions could be subjected to the same modelling process. Let me explain.

Continue reading


Rewatch the Issue 12 virtual launch event

Have you read through all of Issue 12 and feel lost without Chalkdust in your life? Then you are in luck because to celebrate Issue 12 in all its majesty, we hosted a virtual launch event YouTube livestream!

This featured not 1, not 2, not 4, not π, but 3 interactive workshops by the team behind Issue 12.

We figure out whether poetry is really just random nonsense or not, by creating Markov chain poetry and seeing how it measures up (check out this article for more on Markov chains, and this poem for inspiration).

We make our very own stunning mathematical drawings to colour in, using only a ruler and compass (like the ones on issue 12’s cover)—just the soothing activity you will need to take your mind off the fact that it’s another six months until Issue 13.

And last but certainly not least, we play some Countdown (numbers round, of course), presented by Nick Hewer and Rachel Riley (as soon as they return our calls).

Watch it again at youtu.be/egB0WJe-wPs. The launch event was live on Saturday 14 November, 2:00-3.30pm GMT.


Crossnumber winners, issue 11

Hello everyone! It’s time to announce the winners of the Chalkdust prize crossnumber #11! Before we reveal the winners, here is the solution of the crossnumber.

1 0 9 8 9 1 0 9 8 9
1 1 1 1 5 1 2 6 8
5 4 2 0 1 1 9 9
1 5 3 7 9
5 4 4 3 2 2 2 0
8 3 9 8 2 8 9 6 1
7 3 5 1 4 3 2
1 3 5 7 3 1 5 9
2 5 8 7 0 3 5 8
6 5 4 8 5 6 0
1 1 1 3 9 9 1 3 1
0 2 2 2 6 0 2 5
9 7 3 7 0
9 9 1 1 2 0 2 5
8 6 2 1 7 1 1 1 1
9 8 9 0 1 9 8 9 0 1

The sum of the across clues was 10994518584.

There were 74 entries, 65 of which were correct. The randomly selected winners are:

  1. Paul Livesey, who wins a £100 Maths Gear goody bag,
  2. Sam Dell, who wins a Chalkdust T-shirt,
  3. Sarah Corbett, who wins a Chalkdust T-shirt,
  4. George Panagopoulos, who wins a Chalkdust T-shirt.

Well done to Paul, Sam, Sarah and George, and thanks to everyone else who attempted the crossnumber. See you shortly in issue 12…


Chalkdust issue 11 – Coming 17 April

The cover of issue 11

The cover of issue 11

The schools are shut, the universities closed, and the nation is in lockdown—what better time to publish a magazine? Save the date because we are publishing Chalkdust issue 11 at 9am on Friday 17 April. This issue includes all of your favourites like Dear Dirichlet, What’s hot and what’s not, and the crossnumber. There is also a smörgåsbord of articles to delight your mathematical senses, and of course terrible handcrafted maths puns, the like of which you can’t find anywhere else.

Due to current circumstances we will initially publish issue 11 online only: the articles will be available on the website, and (as usual) you will be able to read the whole magazine on issuu or download a PDF. We will be printing and distributing physical copies when circumstances allow. Continue reading


Crossnumber winners, issue 10

Hello everyone! It’s time to announce the winners of the Chalkdust prize crossnumber #10! Before we reveal the winners, here is the solution of the crossnumber.

1 0 8 9 0 2 2 2 2 2 2 2 2 2
1 9 5 2 8 6 7 5
1 0 8 9 5 2 5 8 6
1 9 7 5 4 3 2 0 4 1 2
0 0 5 4 1 1 9 1 0
0 1 0 7 9 6 7 8 9 6 3 0 1
4 2 1 9 8 1 0
8 9 1 8 7 1 6 5 1 4 3 1 2 1 1
1 4 7 2 0 1 0
7 4 5 6 3 4 1 2 3 5 9 4 9
8 4 5 5 5 9 4 9 9
8 9 1 2 6 1 8 1 6 9 9
2 4 9 5 1 1 0 8 9
8 5 2 4 9 9 8 0
2 2 2 2 2 2 2 2 2 1 0 8 9 0

The sum of the across clues was 891873821817653.

There were 40 entries, 37 of which were correct. The randomly selected winners are:

  1. Laurence, who wins a £100 Maths Gear goody bag,
  2. Robert Hannan, who wins a Chalkdust T-shirt,
  3. James, who wins a Chalkdust T-shirt,
  4. Thomas Smith, who wins a Chalkdust T-shirt.

Well done to Laurence, Robert, James and Thomas, and thanks to everyone else who attempted the crossnumber. See you shortly in issue 11…


On curvature: cars, clothoids and cartography

Rollercoasters and railways were originally created without using curvature calculations. People on them would experience undesirable jerk (a sharp change in curvature results in jerk or centripetal forces). You may still experience this on old railways. The image below depicts a centrifugal railway that was constructed in 1846. Nowadays, rollercoaster and railway designers use a type of curve called a clothoid or Euler spiral to make the change in curvature less abrupt, for example when riding a loop-the-loop. I will later mention a couple of applications of Euler spirals. So curvature is clearly an important concept. Let’s get to grips with how it works, and where we should consider it. Continue reading


Book of the Year 2019

A few weeks ago, we announced the 9 book shortlist for the 2019 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 2019

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 its appeal to both mathematicians and non-mathematicians. And the winner is:

The Maths of Life and Death

Kit Yates

This book (Amazon UK, Waterstones), as its title suggests, is all about the maths of life and death. It looks at the maths related to law, biology, medicine, the spread of diseases, and many more areas. Kit takes you through these areas with a series of interesting and well-written stories.

You can read our full review of The Maths of Life and Death here.

Chalkdust Readers’ Choice 2019

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:

A Compendium Of Mathematical Methods: A handbook for school teachers

Jo Morgan

This book (Amazon UK, Waterstones, Foyles) contains details of various methods of completing various mathematical tasks, including subtraction, multiplication, simplifying surds, and polynomial division. Each method is demonstrated by example and reasons why each method works are discussed. This book is an excellent reference for secondary teachers, as well as an interesting book to browse through for the mathematically curious.

You can read our full review of A Compendium Of Mathematical Method here.


The Hidden Half

Michael Blastland is a writer and broadcaster, and was the creator of BBC Radio 4’s More or Less. His book The Hidden Half: How the World Conceals its Secrets (Amazon UK, Waterstones), looks at how to understand, and how to avoid misunderstanding statistics and research.


This book is less of a maths book than many of the books on our shortlist, and much that is discussed relates to science in general. But, as More or Less fans might expect from its creator, an awful lot of its content is related to statistics and evidence; enough that we here at Chalkdust have deemed this a maths book.

In The Hidden Half, Michael Blastland takes the reader through statistical and numerical ideas that most often lead to confusion: relative and absolute risks, the difficulty of comparing now with the past, and the effect of hidden factors. He takes you through each idea with a series of stories illustrating the effect and importance of each idea.


The book begins with a story about marmorkrebs: a species of crayfish that can reproduce asexually, leading to their offspring being clones. Even though both the nature (genes) and nurture (enviroment) of the offspring could be kept the same for each child, there were still surprising differences in the appearance, size, and even internal organs of these offspring. From the go, this story had me hooked, and was a great illustration of an extra hidden causal factor.


This book looks at problems of the misinterpretation of statistics from the point of view of a scientist or economist, giving the effects of this misinterpretation a very real feel.


I really enjoyed this one, and would strongly recommend it to many of my friends, especially my more science-liking (and less maths-loving) friends who would find themselves enjoying this before really realising that the ideas they’re reading about are mathematical. This makes for a very enjoyable read for a mathematician who will not be familiar with the stories that Michael tells.


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 2019 Readers’ Choice. Voting closes at 5pm on Wednesday 26 February.

What is your favourite book on the 2019 Book of the Year shortlist?

  • A Compendium Of Mathematical Methods: A handbook for school teachers by Jo Morgan (48%, 37 Votes)
  • Geometry Puzzles in Felt Tip: A compilation of puzzles from 2018 by Catriona Shearer (18%, 14 Votes)
  • Humble Pi: A Comedy of Maths Errors by Matt Parker (16%, 12 Votes)
  • So You Think You’ve Got Problems? by Alex Bellos (5%, 4 Votes)
  • The Art of Logic by Eugenia Cheng (4%, 3 Votes)
  • The Hidden Half by Michael Blastland (3%, 2 Votes)
  • Maths on the Back of an Envelope by Rob Eastaway (3%, 2 Votes)
  • The Maths of Life and Death by Kit Yates (3%, 2 Votes)
  • Here Come the Numbers by Kyle D Evans and Hana Ayoob (1%, 1 Votes)

Total Voters: 77

Loading ... Loading ...

Maths on the Back of an Envelope

Rob Eastaway is a recreational mathematician, author, speaker, and maths event organiser. His latest book, Maths on the Back on an Envelope (Amazon UK, Waterstones, Maths Gear (signed)), is all about how to (roughly) calculate pretty much anything.


Maths on the Back on an Envelope is an easy-going and enjoyable read. It takes the reader through some methods of approximation of numbers, while showing the reader why being able to perform such approximations is a useful skill. As well as suggesting the use of approximation to check that the correctness of answers, or to work out the approximate size of answer that should be expected, the book also makes the very good point that often an approximation is the best that we can do, and giving answers to a greater-than-appropriate level of accuracy can be misleading.


The book explains the methods of approximation in a very understandable manner, and also justifies their use and appropriateness. Throughout, the user is challenged to try out their newly found calculation skills; the solutions to these challenges are given the back of the book, alongside some discussion of some ways people go about answering them.


The discussion of estimation and accuracy in this book is very strong, and is not something I’ve read much about elsewhere. The book sets itself apart from other books by encouraging you to actively engage in tasks related to the material being discussed, and you may find yourself finishing it with a far greater understanding of what everyday numbers mean.


Although many of the methods of mental or on-paper calculation discussed in this book will be familiar to the keen mathematician, this book is still an enjoyable read, and even the most capable calculator can benefit from thinking about the issues surrounding accuracy in this book. I’d most strongly recommend this book to those looking to improve their skills with numbers, or to improve their understanding of numbers around them an in the news, but there’s still plenty to enjoy here for others.