6 ms·
Amateur Mathematician Finds Smallest Universal Cover
- caf 8y agoThis form of problem reminds me a little of the Sofa Problem (although there you are maximising rather than minimising).
- olooney 8y agoYes, and it has the same kind of "decades of slow incremental improvements by shaving corners off" kind of vibe. https://en.m.wikipedia.org/wiki/Moving_sofa_problem https://en.m.wikipedia.org/wiki/Moving_sofa_problem
- Phemist 8y agoIf you check the wikipedia page, it seems that Philib Gibbs has contributed to this problem as well: '''A computation by Philip Gibbs produced a shape indistinguishable from that of Gerver's sofa giving a value for the area equal to eight significant figures.[6] This is evidence that Gerver's sofa is indeed the best possible but it remains unproven. '''
- caf 8y agoI wonder if anyone sells an actual (Conjectured) Optimal Sofa.
- Sniffnoy 8y agoNote: Smallest known universal cover. It isn't proved optimal (and probably isn't). Also, the title here is a little confusing as this has nothing to do with universal covers in the usual (topological) sense; this is about Lebesgue's universal covering problem[0], a problem in plane geometry. [0]https://en.wikipedia.org/wiki/Lebesgue%27s_universal_covering_problem https://en.wikipedia.org/wiki/Lebesgue%27s_universal_coverin...
- dumbfoundded 8y agoI find it interesting that this problem has no real application and the resulting cover seems pretty ugly given how basic and fundamental the question seems.
- tantalor 8y ago> no real application Yes, welcome to math.
- dumbfoundded 8y agoMath has lots of applications. Computer science is basically just applied discrete maths.
- zwkrt 8y agoIt's interesting that the area he removed was asymmetric; my intuition would be that the optimal solution would be symmetric.
- thaumasiotes 8y agoHis methodology was to generate random shapes, fit them into the existing best known cover, and then shift them toward one of the corners; once you know that, it's unsurprising that he only removed area from the opposite corner.
- timjver 8y agoI think the lack of left-right symmetry was the surprising bit.
- level3 8y agoIt’s not as surprising when you realize that the problem allows reflections of the shape, removing the need for a symmetrical cover. There are lots of lopsided shapes that will barely fit on one side but leave room on the other. With an asymmetrical cover you can handle different classes of shapes with each side, while a symmetrical cover ends up overcompensating and being too “one size fits all.”
- RantyDave 8y agoAmateur Mathematician. Who has a degree in maths from Cambridge.
- vecter 8y agoThis shouldn't be surprising. You pretty much need formal training in mathematics of some sort to be able aspire to even be an amateur mathematician. There are many people with math degrees out there, it's just that most didn't pursue careers in mathematics.
- IshKebab 8y agoMost people who get maths degrees from Oxbridge don't go on to be professional mathematics though. Out of the 7 I know only one did. The others basically don't do complex maths anymore.
- mabbo 8y agoIn the sense that this person does not do maths as their full time job. Most folks writing papers and finding new proofs, etc, do.
- esotericn 8y agoAn amateur is not a person that has no knowledge. An amateur is a person who pursues an activity independently of their source of income. It's kind of amusing that general understanding of the term has flipped in this way - basically it implies that if you're not doing something under a capitalistic structure, you're probably doing something wrong. A bunch of software that you use on your computer on an everyday basis was produced by amateurs. Hobbyist might be a better term. I have a degree in Physics. I'm not even an amateur physicist - I don't really do anything in the field at all, my time is spent moving pixels about on screens. :P
- pjungwir 8y agoIndeed, amateur means "lover".
- Sniffnoy 8y ago
- sago 8y agoFascinating that the methodology used to generate these covers is local optimisation. The shape is still fundamentally the one suggested 100 years ago, with "bits lopped off". Which immediately suggests the possibility that they are iterating towards a local minimum. Is the space of solutions smooth enough to have any confidence that there aren't better places to start?