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Amazing Sierpinski Tetrahedron

In the wake of a flurry of tetrices being constructed in schools all over the country (see this post about fractal Christmas tree worksheets, and this post featuring photos of completed trees), we’ve also been sent a video of a school group constructing an ambitious and impressive fractal structure, using envelopes cleverly folded into tetrahedra. The video is below, and features (eventually) a level 5 Sierpinski Tetrahedron, made from 1024 envelopes!

Via teacher Tim Dolan on Twitter.

Fractal Christmas Trees – Your Photos

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.

Math Professor Invents Non-Reversing Mirror

Andrew Hicks, a professor at Drexel University, has invented a new type of curved mirror which shows the reflection without inverting it left-right, as normal plane mirrors do. Although this effect can be achieved by placing two mirrors at right angles and looking at them both along the 45 degree bisector (as anyone who’ve ever stayed on a canal boat or similarly small bathroom which uses a double-mirror in the corner will attest – it’s mildly disconcerting), this new invention is a single curved piece of glass. Apparently, some maths is involved: Hicks has “design[ed] computer algorithms to cleverly manipulate the angles of curved mirror surfaces so distortions in the reflection are precisely controlled”.

Matt Parker’s Fractal Christmas Tree

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.

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.

Registration for the Alan Turing Cryptography Competition 2013 is open

Following on from the huge success that was their inaugural competition earlier this year, mathematicians from the University of Manchester have put together another Cryptography Competition in honour of father of modern everything, Alan Turing.

This time, the competition is open to teams of school children from all over the UK, and comprises a six-chapter story featuring Alice and Bob Mike and Ellie, who get “caught up in a cryptographic adventure”. Solving all the puzzles and cracking the codes faster than other people gets you on the leader board, and there are prizes for being near the top as well as extra prizes for randomly-selected teams who’ve solved everything. (You know that since it’s a maths department, their randomisation algorithms will be top-notch). It’s also possible to enter as a non-schoolchild, and check your answers on the site, although you won’t be eligible for prizes. The competition is aimed at UK school years 7-11 (age 11-16), although I can confirm it’s dead good fun for anyone interested in cryptography puzzles themed around exciting storylines.