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Friend of the Aperiodical James Grime made this video in 2009 discussing the arithmetic of the Twelve Days of Christmas song. Watch carefully and you might spot in the background the picture he keeps of himself that ages in his place.
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Statistics of the year 2018
The second annual Royal Statistical Society ‘statistics of the year’ have been announced. The Guardian reports that these include top prize for “90.5%, the proportion of plastic waste that has never been recycled”, and that other statistics awarded or commended involve Jaffa Cakes, poverty, gender equality, climate change and someone called Kylie Jenner. The RSS says “the Statistics of the Year aim to show the sometimes surprising stories that numbers can tell us about the world”.
Statistic of the year from the RSS.
Environment, Jaffa Cakes and Kylie Jenner star in statistics of year, at The Guardian.
Aperiodvent, Day 18: Polyomino-ho-ho
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In what could be the most tenuous festive connection so far, we’ve found this lovely paper on folding polyominoes from other polyominoes. Maybe something to keep you occupied over those few days when all the festivities are over and everyone’s just sitting around eating chocolates… and playing with the foil wrappers?
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
Byrne’s Euclid recreated for the web
This is astonishing. Designer and ‘data geek’ Nicholas Rougeux has painstakingly recreated all six books of Oliver Byrne’s Euclid on the web, following the original as closely as possible while adding links between propositions and even making the diagrams interactive.
Aperiodvent, Day 17: Christmas Stockings in Pascal’s Triangle
If you’re familiar with Pascal’s triangle, you’ll know it has a lot of brilliant hidden patterns and features. One of my favourites is the Christmas Stocking Identity, also more prosaically called the Hockey Stick Identity. The identity states:
$$ \sum_{i=r}^n \binom{i}{r} = \binom{n+1}{r+1} \qquad \textrm{ for } n, r \in \mathbb{N}, n > r $$
This means that if you follow a diagonal line downwards into the triangle and add the terms you encounter, the sum will be equal to the term just off the diagonal wherever you stop. This is shown in this diagram, where you can see that:
$1 + 6 + 21+ 56 + 126 + 252 = 462$
To celebrate this fun and festive fact, I’ve put together a PDF you can print and cut up to demonstrate this, by sliding the holes around over the triangle. Enjoy!
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
Aperiodvent, Day 16: Relatively Prime Christmas Special
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Remember this time last year, when we had a chat with Samuel Hansen for their amazing Relatively Prime podcast? We discussed our collective hobby of getting angry at stupid formulae in the news, and how it sometimes crosses over with the festive season. Listen again below.
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
Aperiodvent, Day 15: Mathematical Present Wrapping video
In the viral YouTube hit of Christmas 2015, Katie Steckles demonstrates some of the most mathematically satisfying ways you can wrap your Christmas presents.