The Aperiodical 

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The permutation clock

By Christian Lawson-Perfect. Posted August 29, 2020



I recently had an idea: map the Unix time (seconds since 1st January 1970) to shufflings of a deck of cards. Each second would correspond to a different ordering of the 52 cards.

I wanted to think about how mind-bogglingly huge $52!$ is: $52!$ seconds is more than $2 \times 10^{60}$ years. So even if you spent your entire life watching this thing, you’d leave this world having seen basically none of the possible permutations. Happily, Wikipedia reckons that the heat death of the universe will happen in about $10^{100}$ years, so there’s plenty of time for me to enact my plan.

Aperiodical Round Up 11: more than you could ever need, want or be able to know

By Christian Lawson-Perfect. Posted August 28, 2020



Hello, my name’s Christian Lawson-Perfect and my main mathematical interest is “everything”.

Before The Aperiodical existed as its own thing, the only outlet I had for my mathematical eclecticism was a series of posts on the Acme Science blog called Aperiodical Round-Up. Eventually I stopped writing them, as work and family took up more of my time. This post has been sitting in The Aperiodical’s drafts folder for six years. Time to finish it!

Let’s begin with the first 10,000 digits of π dialled on a rotary phone.

Resources for learning probability and statistics

By Katie Steckles. Posted August 18, 2020

I was recently asked for some recommendations of resources for learning about probability and statistics, for someone without a strong mathematical background. I did a little digging, and have collated what I found here in case it’s useful to anyone else. Add your own suggestions in the comments!

Carnival of Maths 184

By Katie Steckles. Posted August 4, 2020

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of July, is now online at Tom Rocks Maths.



The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

nimsticks: LaTeX package for drawing Nim sticks and games

By Peter Rowlett. Posted July 24, 2020

A while ago on this blog I shared a LaTeX macro I had written for drawing games of Nim. I have now taken the plunge and written this into a LaTeX package called nimsticks. (Why? What do you do to relax on a lazy Sunday morning?)

Here is the description of the nimsticks package:

This LaTeX package provides commands \drawnimstick to draw a single nim stick and \nimgame which represents games of multi-pile Nim. Nim sticks are drawn with a little random wobble so they look ‘thrown together’ and not too regular.

What this does it allows commands such as \nimgame{5,3,4} which renders like this:



From the mailbag – circles of circles

By Katie Steckles. Posted July 14, 2020

Katie’s dad needs a little maths advice – so he’s asked his daughter for some help, and she’s used it as an excuse to go on about maths for a while, as usual.

Dear The Aperiodical,

I’ve been working on a scale model of an underground mine, which will be lit using fibre optics – thin cylindrical strands of clear material, which can transmit light from a source at one end and output light at points all over the model.

All the strands will come together behind the scenes and be pointed at a light source inside a box – but if I have 24 strands with circular cross-section, each 1.5mm in diameter, how big a hole would I need to drill in the box for all the strands to pass through?



Carnival of Maths 183

By Katie Steckles. Posted July 6, 2020

The next issue of the Carnival of Mathematics, rounding up blog posts from the month of June, is now online at Famous Mathematicians.



The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.