Sconic sections

This is a strange one: How to make edible conic sections! You can find the details at Evil Mad Scientist. If you enjoy maths-related cooking, then see my post on Tau-nados. Does anyone else have any other...

Matt Parker Number Ninja...

This is mainly one for those local to Leeds (although see the bottom of the post). As part of the Leeds Festival of Science, Matt Parker will be giving a talk at the University. From the advertising: Direct from BBC Radio 4’s Infinite Monkey Cage with Brian Cox and Robin Ince, with research featured on QI, Leeds will be welcoming stand-up Maths comedian Matt Parker. Expect everything from debunking number nonsense and flagrant sudoku abuse to the mysterious patterns in the locations of ancient monuments and defunct Woolworths stores. Suitable for ages 16 plus. Entry to the show is strictly by ticket only. Book early as places are limited. Tickets can be booked via the University of Leeds website I’ll be doing my own little bit for Leeds Science Week with a visit to at least one school. See the Schools Programme. Teachers and pupils: Although it’s too late to book me for science week, if you want me to visit your school, then get please get in touch. I’ll travel further afield than just...

Mathematics of the mosh pit...

Rock music fans are aware of the phenomenon of the mosh pit at concerts — a riotous area, usually close to the stage, where concert-goers, in lieu of learning complicated dance steps, slam violently into each other (and hence an alternative name for moshing is slam dancing). Until now the fascinating mathematics of this emergent property of crowds has been unjustly ignored. However, this has changed with the advance publication on the arXiv Collective Motion of Moshers at Heavy Metal Concerts by Silverberg, Bierbaum, Sterna and Cohen. The abstract states Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models. The authors model the behaviour of the mosh pit (and circle pit), provide source code and Java script interactive moshpit The conclusions will be surprising to many: If we increase the self-propulsion coefficient (decrease ), we find the motion, though random, is no longer fit by a Maxwell-Boltzmann distribution. Instead, collisions between active and passive MASHers [Mobile Active Simulated Humanoid] on the boundary of the simulated mosh pit removes energy faster than collisions among active MASHers can rethermalize the system. Consequently, measurements in silico show a radial temperature gradient is established with a higher effective temperature at the core of the simulated mosh pit and a lower effective temperature at the edge A valuable and timely addition to the literature. Ok, let’s...

Archimedes and 3D printing...

3D printing seems to have some sort of turning point in the last few months. Lots of people know what it is and many are experimenting with it. This week I began teaching on my History of Mathematics module; yesterday’s lecture was about Archimedes. I would never imagined that the two could be combined but today I saw a preprint on the arXive on the combination of Archimedes and 3D printing. The paper has a brief history of Archimedes and his works (and quite a few elementary typos) and focusses on how to make models of his inventions, for example his water screw, and more mathematical objects using a 3D printer. I don’t have access to 3D printing but would be intrigued to give some of the Archimedes models a go. Certainly, it would be great to have a supply of Platonic and Archimedian solids to show students. Has anyone out there tried something...

Mathematics of Lego

Obviously the first post of the year should be a serious one about the year ahead, New Year’s resolutions and such. Not this time. This time I urge you to have a look at the mathematics of Lego via Wired. Read the article here. To be honest I’m not sure if this really is a good example of a log-log plot (could I use it in class) or if it even tells us something deep about Lego but I think it’s worth a...

Painting by numbers – restoring frescoes...

You may have seen in the news this week that an elderly amateur attempted the restoration of a religious fresco. The result is pictured below. I took the picture from the BBC article that you can read here. By coincidence this week I saw an article by Carola-Bibiane Schönlieb on the mathematical technique of inpainting. This allows restoration of damaged pictures by using some mathematical process to fill in the damaged part. A particular common method is to use diffusion equations – the idea is that we use something like the heat equation. Imagine the ink on the border of the damaged region as being like heat and the heat travels into the region through conduction. Compare the two images below take from a preprint by Schönlieb and others. The top one is a vandalized picture and the bottom is the version restored through a diffusion equation method. Most people probably wouldn’t realize that the picture had been repaired unless they’d been told. Schönlieb and others have worked on restoring the following Austrian fresco Here’s a picture of the proposed restoration (unfortunately only in black and white): The pictures come from a paper which contains the details. The article I saw this week is more accessible and can be read in the Matlab Mathworks...