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A new pyramid-like shape always lands the same side up

quantamagazine.org

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Re: A new pyramid-like shape always lands the same side up

#71

Post by eszed »

GuB-42 wrote: post #25
malnourish wrote: post #11

Earlier quoted context omitted.

Simple invention made possible by sophisticated precision manufacturing.

I think it is a very underestimated aspect of how "simple" inventions came out so late. An interesting one is the bicycle. The bicycle we all know (safety bicycle) is deceivingly advanced technology, with pneumatic tires, metal tube frame, chain and sprocket, etc... there is no way it could have been done much earlier. It needs precision manufacturing as well as strong and lightweight materials for such a "simple" id…

To support your point, and pre-empt some obvious objections:

- I've ridden a bike with a bamboo frame - it worked fine, but I don't think it was very durable.

- I've seen a video of a belt- (rather than chain-) driven bike - the builder did not recommend.

You maybe get there a couple of decades sooner with a bamboo penny-farthing, but whatever you build relies on smooth roads and light-weight wheels. You don't get all of the tech and infrastructure lining up until late-nineteenth c. Europe.

Re: A new pyramid-like shape always lands the same side up

#72

Post by ChuckMcM »

gus_massa wrote: post #55
ChuckMcM wrote: post #16

Worst D-4 ever! But more seriously, I wonder how closely you could get to an non-uniform mass polyhedra which had 'knife edge' type balance. Which is to say; 1) Construct a polyhedra with uneven weight distribution which is stable on exactly two faces. 2) Make one of those faces much more stable than the other, so if it is on the limited stability face and disturbed, it will switch to the high stability face. A struc…

A solid tall cone is quite similar to what you want. I guess it can be tweaked to get a polyhedra.

So a cone sitting on its circular base is maximally stable, what position do you put the cone into that is both stable, and if it gets disturbed, even slightly, it reverts to sitting on its base?

Re: A new pyramid-like shape always lands the same side up

#74

Post by Cogito »

gerdesj wrote: post #61
boznz wrote: post #2

maybe they should build moon landers this shape :-)

Or aeroplanes. Not sure where you put the wings. Why restrict yourself to the Moon?

Recent moonlanders have been having trouble landing on the moon. Some are just crashing, but tipping over after landing is a real problem too. Hence the joke above :)

Re: A new pyramid-like shape always lands the same side up

#76

Post by gerdesj »

Cogito wrote: post #74
gerdesj wrote: post #61

Earlier quoted context omitted.

Or aeroplanes. Not sure where you put the wings. Why restrict yourself to the Moon?

Recent moonlanders have been having trouble landing on the moon. Some are just crashing, but tipping over after landing is a real problem too. Hence the joke above :)

Mars landers have also had a chequered history. I remember one NASA jobbie that had a US to metric units conversion issue and poor old Beagle 2 that got there, landed safely and then failed to deploy properly.

Re: A new pyramid-like shape always lands the same side up

#78

Post by zuminator »

robinhouston wrote: post #42
zuminator wrote: post #37

Earlier quoted context omitted.

That article doesn't prove what you say that it does. It just proves because a perpetuum mobile is impossible, it is trivial that a polyhedron must always eventually come to rest on one face. It doesn't assert that the face-down face is always the same face (unistable/monostable). It goes on to query whether or not a uniformly dense object can be constructed so as to be unistable, although if I understand correctly G…

It sounds as though you're talking about the solution to part (b) as given in that reference. Have a look at the solution to part (a) by Michael Goldberg, which I think does prove that a homogeneous tetrahedron must rest stably on at least two of its faces. The proof is short enough to post here in its entirety: > A tetrahedron is always stable when resting on the face nearest to the center of gravity (C.G.) since it…

Ah, I see. I saw that but disregarded it because if it's meant be an actual proof and not just a back of the envelope argument, it seems to be missing a few steps. On the face of it, the blanket assertion that at least two faces must be stable is clearly contradicted by these current results. To be valid, Goldberg would needed at least to have established that his argument was applicable to all tetrahedra of uniform density, and ideally to have also conceded that it may not be applicable to tetrahedra not of uniform density, don't you think?

This piqued my curiosity, which Google so tantalizingly drew out by indicating a paper (dissertation?) entitled "Phenomenal Three-Dimensional Objects" by Brennan Wade which flatly claims that Goldberg's proof was wrong. Unfortunately I don't have access to this paper so I can't investigate for myself. [Non working link: https://etd.auburn.edu/xmlui/handle/10415/2492 ] But Gemini summarizes that: "Goldberg's proof on the stability of tetrahedra was found to be incorrect because it didn't fully account for the position of the tetrahedron's center of gravity relative to all its faces. Specifically, a counterexample exists: A tetrahedron can be constructed that is stable on two of its faces, but not on the faces that Goldberg's criterion would predict. This means that simply identifying the faces nearest to the center of gravity is not sufficient to determine all the stable resting positions of a tetrahedron." Without seeing the actual paper, this could be a LLM hallucination so I wouldn't stand by it, but does perhaps raise some issues.

Re: A new pyramid-like shape always lands the same side up

#79

Post by emporas »

boznz wrote: post #2

maybe they should build moon landers this shape :-)

They could do that, but a regular gomboc would be totally fine. There are no rules for spaceships that their corners cannot be rounded.

Maybe exoskeletons for turtles could be more useful. Turtles with their short legs, require the bottom of their shell to be totally flat, and a gomboc has no flat surface. Vehicles that drive on slopes could benefit from that as well.

Re: A new pyramid-like shape always lands the same side up

#80

Post by ofalkaed »

MPSimmons wrote: post #60
ortusdux wrote: post #39

Earlier quoted context omitted.

You jest, but I knew a DND player with a dice addicting that loved showing off his D-1 Mobius strip dice - https://www.awesomedice.com/products/awd101?variant=45578687... For some reason he did not like my suggestion that he get a #1 billard ball.

I've always seen a D1 as a bingo ball...

You sunk my battleship!
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