### Curvahedra Geometry

Longtime friend of the Aperiodical, artist, mathematician and #BigMathOff semifinalist Edmund Harriss has come up with a new puzzle/toy/exploration set, developing his Curvahedra system. We asked him to explain the maths behind it in this guest post.

Curvahedra is a flexible system of connectors that can make all sorts of different things, combining puzzles (and self-created puzzles) with art. You can get your own to play with, explore, prepare for Christmas (they make great decorations, wreaths and presents) at our online store, and get 15% off with the discount code APERIODICAL.

As this is the Aperiodical, you might be most interested in how it can be used to explore mathematics. In the big math off I talked about the basic ideas behind the system, Gauss’ famous Theorema Egregium and Gauss-Bonnet theorems. A really simple version of this comes from just considering triangles, that can be built up to make this:

### Armadillo Vault held together only by friction

via math-fun.

### There was a “beauty of maths” garden at the Chelsea Flower Show. Yeah, sure, why not

The Winton Beauty of Mathematics Garden was an entry in this year’s Chelsea Flower Show. It looks like this:

Photo from Winton Capital, via The RHS on Twitter.

Apparently those symbols winding their way around the garden are “plant growth algorithms”, whatever those are.

There’s also a golden-ratio-thingy water feature, of course.

You can thank Winton Capital, sponsors of all sorts of worthy maths projects, for this bit of mathsy art.

### Messiaen’s “Quartet for the end of time”, animated by Simon Russell and Marcus du Sautoy

Marcus du Sautoy has teamed up with animator Simon Russell to create this animatino to accompany Messiaen’s Quartet for the end of time. It’s got all the usual arty maths things in it – the Fibonacci sequence and golden ratio, prime numbers, polygons and polyhedra of all sorts – as well as the less well-trodden sporadic group $M_{12}$. It all comes together quite nicely, though I much prefer the elegant end to the spiky-frenetic start.

There’s a page describing all the maths ideas to be found in the video at Sinfini Music.

via Marcus du Sautoy and Sinfini Music on Twitter

### Tessellation Art by Chris Watson

Chris Watson has written in to tell us about his site, Tessellation Art, where he sells his heavily Escher-inspired prints. They’re available in a range of sizes and media, and quite affordably priced. I particularly like the print above, titled Vortex.

### Le Livre de l’Incomplétude is a lovely take on incompleteness

This is a really nice idea. Le Livre de l’Incomplétude (The Book of Incompleteness) is an “artistic appropriation of Gödel’s incompleteness theorem,” initiated by artist Débora Bertol. The superficial understanding of that theorem is that every consistent formal theory contains truths which can’t be proved inside that theory, so the book’s conceit is that it will catalogue as many different arithmetic formulas as possible that evaluate to each of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

I think it’s a really charming take on one of the most abstract and hard-to-understand subjects in maths.