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Aperiodvent, Day 4: Möbius Paper Chains

By Katie Steckles. Posted December 4, 2018

Möbius Paper Chain photo by SpaceLlamaMK1 on Imgur

If you’re trying to think of ways to decorate your home, office or classroom, look no further than mathematically non-trivial paper chains, made from Möbius bands.

All you need is some double-sided coloured paper (ideally the same colour on both sides, but if you want to show off the twist, you can go two-tone) cut into long strips, and tape to loop them together.

If you consistently use the same handedness of Möbius loop (twisting the same way each time) your chains will hang nicely, and they’ll all sit in the same orientation – unlike those messy normal paper chains, where every second loop is at right angles.

Share your photos of finished Möbius paper chains on Twitter, mentioning @Aperiodical, and we’ll retweet the best.

This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.

Aperiodvent Day 3: Mince Pi Pendulum

By Katie Steckles. Posted December 3, 2018

Today’s contribution is from friend of the site, Festival of the Spoken Nerd’s Matt Parker, who’s found a way to approximate π using a mince pie (or any type of pie, or indeed any small object with non-zero mass, but the mince pie is the most festive option). The trick is to use it as the weight on the end of a 2.45m-long pendulum, and time the swings.

The pendulum is part of the latest Spoken Nerd show, You Can’t Polish a Nerd (which we’ve reviewed here recently), and this clip shows Matt’s preparations to do the approximation live on stage:

https://twitter.com/FOTSN/status/1062402096572575744

The diagram below outlines how it’s done:

The period of a pendulum is a complete swing back & forth.
Period time = $2\pi \sqrt{\frac{\textrm{length}}{g}}$
Acceleration due to gravity on the Earth’s surface is about: $g = 9.8m/s^2$
If the length of a pendulum is $\frac{9.8}{4} = 2.45m$ the period will be $\pi$ seconds.
PRO TIP: For greater accuracy: leave your pi-endulum swinging for a while and divide the total time by the number of swings to get $\pi$.

Share your own photos, videos and approximations to mince π on Twitter, and give @FOTSN a mention so they can see just what they’ve started. Visit the FOTSN shop to get your hands on the show in various formats (great Christmas presents!).

This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.

Aperiodvent Day 2: Sprouts

By Katie Steckles. Posted December 2, 2018

Did you know there’s a mathematical game called Sprouts? It’s a game played by drawing dots and lines on paper, and while it seems simple, there’s actually some interesting maths – graph theory and game theory – behind it. According to Wikipedia:

The game is played by two players, starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to itself) and adding a new spot somewhere along the line. The players are constrained by the following rules.

The line may be straight or curved, but must not touch or cross itself or any other line.

The new spot cannot be placed on top of one of the endpoints of the new line. Thus the new spot splits the line into two shorter lines.

No spot may have more than three lines attached to it. For the purposes of this rule, a line from the spot to itself counts as two attached lines and new spots are counted as having two lines already attached to them.

[…] The player who makes the last move wins.

There’s a variant of the game called Brussels Sprouts, which involves drawing a cross instead of a dot somewhere on the line, creating two endpoints, and lines must join two endpoints – but this game is mathematically less interesting (the number of crosses initially entirely determines who will win).

For those who take Christmas super seriously, this paper by Ricardo Focadi and Flaminia Luccio outlines the history of the game, some ways to analyse it using graph theory, and winning strategies.

This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.

Aperiodvent Day 1: Other Mathematical Advent Calendars

By Katie Steckles. Posted December 1, 2018

In what can only be described as a poor marketing move, here are some recommendations for other mathsy advent calendars around the internet.

For teachers and students, and anyone else really, the wonderful NRICH produce two advent calendars of great activity ideas – one for Primary and one for Secondary.
Friend of the site and Chalkdust honcho Matthew Scroggs produces an advent calendar of torturous puzzles on his website. In last year’s calendar, each day had a number puzzle and there was an overall logic puzzle connecting them all. We can’t wait to see what happens this year!
Based on a daft suggestion, I made this printable calendar a few years ago, which assuming you open the correct window each day maintains complete accuracy and also the appropriate level of excitement (there’s an exclamation mark behind each window), which is all you can ask for really.
For the ultimate binary advent calendar, check isitchristmas.com every day in December. It’s either Christmas or it isn’t.

This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.

Aperiodvent 2018 – a month of mathematical things

By Katie Steckles. Posted December 1, 2018

We’re planning to reprise our some-but-not-every-yearly advent calendar of mathematical curiosities, starting here on 1st December and proceeding very advent-calendar-like daily thereafter. You’ll see posts appear in our site feed and on Twitter, and we’ll keep this post updated with links to each day’s post. Credit to Number Gossip for the numbery facts.