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!
As part of Puzzlebomb’s commitment to bringing you all puzzles, all the time, we present a special one-off edition, consisting of festive wordplay. Enjoy! Solutions will be posted in roughly a month from now.
Having posted about Matt Parker’s Fractal Christmas Tree last week, we’ve had quite a few photos of completed trees sent in! Here’s a Tony Hart gallery-style roundup of them.
Stand-up Mathematician and all-round maths lover Matt Parker has been busy again, and he’s made a set of free worksheets for teachers (and, of course, interested non-teachers) to assemble paper nets of 3D fractals, including a Menger sponge and Sierpinski tetrahedron (which I’ve just learned is also called a tetrix).
There’s also a sheet for making a delightfully festive/mathematical fractal Christmas tree, with a Menger sponge base, Sierpinski branches and a Koch Snowflake star on top. Presumably those interested can make Mandelbulb ornaments and Cantor Set tinsel to hang on it. Don’t ask me how that would work.
The worksheets can be downloaded from Matt’s Think Maths website.
Anyone who successfully builds the whole thing: send us a photo and we’ll post it here. Jokes about fractals taking a while to cut out/paint in the comments.
3D printers are ace. People are using them to make all sorts of cool things. If you can describe a shape to a computer, it’s very easy to send that description to a 3D printer, which will happily smoosh some substrates together to make a real model of your shape. Mathematicians are able to describe all sorts of crazy shapes, in exactly the amount of detail computers need, so they’ve taken to 3D printing like ducks to water.
Thingiverse is just a repository for designs, so if you see something you like you’ll have to find your own 3D printer. Shapeways makes the objects and posts them to you; prices can vary from just a few euros to hundreds, depending on the size of the object and the materials used.
As with all other kinds of mathematical art, there’s a huge amount of repetition of the same few ideas, but also a few really interesting and unique designs. I’ve picked a couple of representatives from each of the popular topics, but do search around if you want a version with slightly different parameters; you’re bound to find something suitable.
For the past few months I’ve been quietly compiling a list of interesting mathematical objects I’ve found on the main 3D printing catalogues, Thingiverse and Shapeways. With Christmas approaching, I thought now would be as good a time as any to share what I’ve found.