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Review: Pythagoria

pythagoria

Pythagoria is a puzzle game for PCs. It’s the same idea as Naoki Inaba’s Area Maze: you’re shown a geometric construction, not drawn to scale, and you have to work out a missing length or an area.

Each puzzle is constructed so that it can be solved without ever dealing with fractions, though what exactly that means is up for debate. Whatever it means, it keeps you from breaking out pen and paper to solve a problem algebraically, when you know there should be a way of doing it in your head.

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

Aperiodvent, Day 20: a snowflake sequence

 

a161330_caption

Today’s advent calendar window is covered in snowflakes! These snowflakes aren’t your usual sort, however – they’re made up of thousands of toothpicks arranged into E shapes. Hey, nobody mixes metaphors like mathematicians.

The image above shows 1,124 E-shapes arranged rather artfully. 1,124 is the 32nd entry of the sequence A161330, which lists how many shapes are used at each stage of the construction of the snowflake.

The Online Encyclopedia of Integer Sequences has recently made a page showing off many of the prettier pictures contributors have made to illustrate sequences, of which the snowflake above is just one. The idea is that rather than running their own shop selling t-shirts, you can just grab an image off that page and make your own. How in fitting with the giving season!

This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!

Aperiodvent, Day 16: A tessellating bird

If the song “The Twelve Days of Christmas” had gone up to day 16, that line might have gone “sixteen teals a-tessellating”, and it might look like the above video, made by Chris Watson.

Chris has made some worksheets which can help you make your own tessellations. He also sells his own work at tessellationart.com.

This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!