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Merry Christmas, Aperi-readers. Please enjoy this pleasing algebraic manipulation, and we’ll see you when we’ve finished eating all the mince pies!
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
Merry Christmas, Aperi-readers. Please enjoy this pleasing algebraic manipulation, and we’ll see you when we’ve finished eating all the mince pies!
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
Friend of the site Andrew Taylor has a host of fun gadgets on his website, the Christmassiest of which has to be this Cellular Automata Snowflake Generator. It allows you to iterate two deterministic processes that model aspects of real snowflake generation, and create your own beautiful designs.
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
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If you’re a knitter or crocheter, or just like making things, knitter and mathematician Pat Ashforth has put together a knitting pattern for cube-shaped baubles with the structure of Borromean Rings (each of the three components is linked through the others, and can’t be separated, but if any one of them is cut, the other two are unlinked). There’s a variety of ways to jazz them up, and they’re ideal for using up leftover bits of yarn, as they only need a small quantity.
The cubes can also be used to conceal a small gift. The pattern includes instructions for making the same object from paper/card, or coloured plastic folders.
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
The National Society for the Prevention of Cruelty to Children (NSPCC) has announced 1st February 2019 as ‘Number Day 2019’, saying:
It’s maths, but not as you know it.
Join thousands of schools for a mega maths-inspired fundraising day and raise money for the NSPCC.
Whether you dedicate a day or an hour to being a maths maverick, every pound you raise counts towards our fight for every childhood.
Schools that register get digital resources to use in class, fundraising tips, maths activities, posters and safeguarding teacher resources.
Number Day 2019 at NSPCC.
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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.
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.
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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.