A conversation about mathematics inspired by a box of Christmas crackers. Presented by Katie Steckles and Peter Rowlett. Merry Christmas!
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Every year, Donald Knuth gives a Christmas lecture at Stanford.
This year, he wanted to talk about a conjecture he’s recently investigated.
It’s just over an hour long. Sit down with a warm drink and enjoy some interesting recreational maths from the master.
There seem to be a bumper list of mathematical advent calendars this year, even though the stellar efforts of Katie and Christian’s Aperiodvent Calendar 2015 aren’t being repeated. There aren’t yet enough for an advent calendar with a different mathematical advent calendar behind each door, so we thought a straight round up was the way to go.
Before Christmas, the benign megasurveillance bods at GCHQ released a set of festive puzzles, in the form of a Christmas card and associated website. An initial nonogram puzzle led to a sequence of increasingly fiendish teasers, and solvers of the final set of puzzles were invited to email in their answers, with the correctest winning a fancy paperweight, signed book and, GCHQ were at pains to stress, not an Imitation-Game-style secret job offer.
If you were wondering what happened with all the left-over wrapping paper from this morning’s post about wallpaper groups, Katie has made a YouTube video demonstrating some mathematical quirks of gift wrapping. Enjoy!
Christmas wrapping paper is sold in thousands of different variations, including plain, coloured, patterned, foiled and even flock, but one thing it’ll have in common is that it will repeat whatever pattern it has, regularly across the design.
I’m interested in symmetry, and was intrigued to find a curious fact about the symmetries of such repeating patterns – their symmetries are quite limited.
Internet 3D printing emporium Shapeways has released a nifty little tool to create your own unique Christmas bauble, which they’ll print out and send to you in time for the festive season.
It works by mapping a triangular design onto a blown-out icosahedron, and applying some “kaleidoscope effects”. As far as I can tell, that means they expand and rotate the patterns so they overlap.
There’s a selection of built-in patterns you can choose from, or you can upload your own pattern to make a really unique decoration. However, because the resulting object needs to exist in the real world, you need to take care to make sure it all comes out in one connected piece. Shapeways have written some very clear instructions about how to achieve that.
Play: Ornament Creator from Shapeways
via Vladimir Bulatov on Google+, who seems to work for Shapeways now. Exciting!