First brainstorming ideas
On Friday we had our first session of brainstorming mathematical ideas that could be turned into shirty sculptures. Although there wasn’t a good turnout of mathematicians (academics all seem to be away over the summer!) we had lots of ideas emailed to us beforehand so there was plenty to think about.
Take a look at the ideas below and let us know which ones you like best!
– Cut strips into the back of a shirt and braid them;
– Make a Klein bottle shirt by passing a sleeve through the main shirt and sewing up openings;
– Create an Alexander Horned Sphere using smaller and smaller shirts to create the ‘horns’;
– Use seven shirts of different colours and sew them into a torus to demonstrate that 7 colours are needed so that no two regions of the same colour touch;
– Sew shirts into a network or graph, illustrating a particular problem. For example, making a thrackle and designing an accompanying flash game on this website;
– A hyperbolic shirt, sewing in extra material to the hem or sleeves;
– Design a pattern on the shirt which can only be seen when viewed from a particular angle, illustrating work done on integrable systems where a function only looks linear when transformed into the correct coordinates;
– Sew shirts together to incorporate a particular group structure or symmetry, for example the dihedral group;
– Create a ‘hypershirt’, that is, a 3-dimensional representation of a 4-dimensional hypercube;
– Cut a disc out of the front of a shirt and re-sew to illustrate a solution to a puzzle (how to tile the disc with congruent tiles so that at least one tile does not touch the centre);
– Use stuffing to create a 3-dimensional surface representing a particular statistical distribution;
– Cut a shirt into strips and re-assemble using random rules, for example by throwing dice to determine how many strips of a particular colour are used;
– Find a shirt with widely spaced vertical lines, then sew matchsticks on to find an approximation to pi using Buffon’s needle method;
– Use a t-shirt with a distinctive design and cut parts out of it, asking whether the public can guess what the missing pieces are. Image reconstruction is a big topic being explored by mathematicians in Edinburgh!
– Cut a shirt into strips and re-assemble into a Kakeya set – a picture which contains a line of length 1 in every direction. Amazingly, it is possible to do this so that the picture has as small an area as you want!