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.
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.
In the viral YouTube hit of Christmas 2015, Katie Steckles demonstrates some of the most mathematically satisfying ways you can wrap your Christmas presents.
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If you manage to dismiss all the ads, the blog Happiness is Homemade has a post which shows you how to make a cool dodecahedral star lantern out of paper (and glue, and you’ll need a light source too if you want it to actually function as a lantern).
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
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The fold and cut theorem, which states that, after sufficient folding, any shape made of straight lines can be cut out of a piece of paper in one cut, is probably the most crafts-friendly result in all of maths. Inspired by The Aperiodical’s very own Katie Steckles’ video on the subject, Sam Hartburn has created a handy PDF with instructions for folding and cutting a festive Christmas tree shape.
This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.
The Alan Turing Cryptography Competition, now in its 7th year, is an online competition run by the University of Manchester School of Mathematics, for school students up to year 11 or equivalent. Cryptographic puzzles are released every couple of weeks and teams of up to four compete to solve the puzzles, with prizes for the fastest and other randomly selected correct entries. Registrations are open now, and the competition starts on 28th January 2019.
For sixth form pupils, there is also MathsBombe – an online competition, with two mathematical puzzles released every fortnight. The puzzles are not directly related to the A-Level syllabus but will require students to use their problem-solving skills.