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Misleading title. Other shapes have been well known for years, like a sphere. The novelty here is the first polyhedron that can't pass through itself.
by teo_zero 1y ago
Misleading title. Other shapes have been well known for years, like a sphere. The novelty here is the first polyhedron that can't pass through itself.
- jibal 1y agoconvex polyhedron (but your point about the title is valid)
- cluckindan 1y agoA sphere can be approximated by a polyhedron. Somewhat obviously, all such polyhedra would seem to have the Rupert property. This new Nopert seems to differ in one key detail: some of the vertices near the flat top/bottom are at a shallower angle to the vertical axis than the vertices below/above them. Can you pass the T-shaped tetromino through itself?
- mkl 1y agoThe T-shaped tetromino is not convex, so not part of the conjecture. There are many nonconvex shapes that don't have the Rupert property.
- boothby 1y agoNevertheless, the t-shaped tetronimo (assuming four glued cubes) has a shadow shaped like a bar of length two. I believe that such a shadow will pass through a bar of length three, with a tilt similar to the cube's.
- brabel 1y agoIf the remaining edge has exactly zero thickness , it means it doesn’t fit. I think that would be the case in that example?
- mkl 1y agoIt fits if it is tilted. If the 3-cube bar of the T is tilted 45° there will be a 3×√2 rectangle part of the shadow, which the 1×2 shadow fits through.
- neom 1y agoSomewhat unrelated question, a lot of the folks replying to the parent comment read to me like they're really good at visualizing things in their minds eye, when you talk like this is it because you can think about math really well? Can you visualize what you're saying? Sorry if this question doesn't make sense!
- boothby 1y agoI do not have a mind's eye*, outside of the dimmest, briefest flash of people's faces if I've known them for several years. I do have a peculiarly strong sense of imaginary touch, which gets used when contemplating problems like these. Also, a significant component of my job is arranging things in 3-space. I'd be one of those people who say "I'm good at tetris" while packing a moving truck, but I am not actually good at tetris per se. * https://en.wikipedia.org/wiki/Aphantasia https://en.wikipedia.org/wiki/Aphantasia
- neom 1y agoThank you for your reply. Extremely interesting to me. My thinking and memory is pure motion picture and sound, it makes me think that I could be good at geometry as I can do spatial thinking well, however the downside of my thinking style is I've never been able to find a framework that allows me to hold fine detail symbols in space and work with them usefully, I suppose hence dyslexia + dyscalculia diagnosis. Maybe people like me who are in math use whiteboards and notes a lot or something? Maybe people like me don't go into maths so much. Imagination of touch is also very interesting, I've read about kinetic leaners before, I like to touch things when I'm learning as it helps with the recall later, but absolutely zero sense of touch is present in the recall. Sorry for the massive tangent, I'm just very curious about this stuff!
- debtta 1y agoI don't think that's the case, how can you turn a bar of length two but still have it fit within the width of the bar of length three?
- cluckindan 1y agoThat’s true. I digress, but you could give tetrominos convex hulls, and the result would still be somewhat Tetris-compatible.
- AmbroseBierce 1y agoFor laymen's sake I think the title should say "First shape (without curves) found that [...]"
- bonoboTP 1y agoAnd not "pass through itself" but "pass through its copy"
- KernalSanders 1y agoThe article isn't really for the layperson. It's confusing why several people are nitpicking at the title.
- integralid 1y agoBecause not-laypoeople ale precisely the kind of people who would nitpick the technically incorrect title.
- CoastalCoder 1y agoI'm a lay person w.r.t. this topic, and I assumed the great exposition was meant exactly for persons like me.
- blendergeek 1y agoThis is quanta magazine. It is for lay people. The reason people are "nitpicking" the title is that "shape" is not a technical term. The technical term for what was found is "convex polyhedron". I read so much of the article before I was sure that it was talking about convex polyhedra specifically because the title is so ambiguous.
- ndsipa_pomu 1y agoQuanta Magazine is very much designed for non-technical lay people. From their About page: Quanta Magazine is an editorially independent online publication launched by the Simons Foundation in 2012 to enhance public understanding of science.
- deleted 1y ago
- ekianjo 1y agoWhy wouldn't a sphere pass through itself? The projected shadow has the same size as its diameter
- Reubend 1y agoWouldn't you need a little material "left over" to claim that it can pass through itself? Two spheres of equal size wouldn't work because they would occupy exactly the same space.
- dguest 1y agoYes! The "pass through itself" criteria is the same as "has one shadow that fits entirely inside another shadow". If you allow "one shadow equals another shadow" then it's trivially true for every shape because a shadow equals itself. Note that this "shadow" language assumes a point light source at infinity, i.e. all the rays are parallel.
- smallerize 1y agoThat's trivially true for every shape, so it's probably not interesting in the context of this puzzle.
- the_arun 1y agoI think Sphere is a outlier for this context.
- paulddraper 1y agoYeah I’m confused
- nyrikki 1y agoA polyhedron has the Rupert property if a polyhedron of the same or larger size and the same shape as can pass through a hole in the original polyhedron. A sphere is a surface of constant width, which the polyhedron approximation is not. > The projected shadow has the same size as its diameter Thus this is exactly why the sphere doesn't have the Rupert property.
- hshdhdhehd 1y agoDoes a sphere not pass through itself (with zero margin?)
- stefanfisk 1y agoHow thick would the remaining walls be after you’ve made the hole required?
- hshdhdhehd 1y agoInfinitesimal I guess! You can fit an arbitrarily slightly smaller sphere for vanishing values of smaller.
- rcxdude 1y agoThere needs to be nonzero margin, else the question is pretty trivial.
- hshdhdhehd 1y agoAh yes correct you just use same orientation and you can get anything through itself.
- munchlax 1y agoYou can do it regardless of orientation given you can apply enough pressure