Conway casually tossing out the idea, and then 60 years later someone actually builds it... that's peak math storytelling.
A new pyramid-like shape always lands the same side up
101–110 of 175 posts
Re: A new pyramid-like shape always lands the same side up
#102Worst 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…
Sort of like a mechanical binary state that passively "remembers" if it's been jostled
Re: A new pyramid-like shape always lands the same side up
#103maybe they should build moon landers this shape :-)
"If tipped, will self-right" sounds like exactly the kind of feature you'd want on the Moon
Re: A new pyramid-like shape always lands the same side up
#104Conway casually tossing out the idea, and then 60 years later someone actually builds it... that's peak math storytelling.
Reminds me of when Mendeleev argued that an element that had just been discovered was wrong, and that the guy who discovered it didn't know what he was talking about, because Mendeleev had already imagined that same element, and it had different properties. Mendeleev turned out to be right.
Re: A new pyramid-like shape always lands the same side up
#105So, like my Vans? https://en.wikipedia.org/wiki/Vans_challenge
The tetrahedron is basically the high-fashion Vans of the geometry world
Re: A new pyramid-like shape always lands the same side up
#106Somewhat disappointing that it won’t work with uniform density. More surprising it needed such massive variation in density and couldn’t just be 3d printed from one material with holes in.
But I guess with polyhedra, the sharp edges and flat faces don't give you the same wiggle room as smooth shapes
Re: A new pyramid-like shape always lands the same side up
#107Worst 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…
>useful as a tamper detector If anyone's actually looking for this, check out tilt and shock indicators made for fragile packages. https://www.uline.com/Cls_10/Damage-Indicators https://www.youtube.com/watch?v=M9hHHt-S9kY
These shock watches and tilt watchers are quite expensive. I wonder how much must be the package worth to be feasible to use this kind of protection
Re: A new pyramid-like shape always lands the same side up
#108maybe they should build moon landers this shape :-)
They will only need to ensure that the pointy end does not penetrate the soft surface too much on decent, becoming an eternal pole.
Re: A new pyramid-like shape always lands the same side up
#109Great article! The excitement kind of ebbed early on with seeing the video and realizing it had a plate/weight on one face. "A few years later, the duo answered their own question, showing that this uniform monostable tetrahedron wasn’t possible. But what if you were allowed to distribute its weight unevenly?" But the article progressed and mentioned John Conway, I was back!
Made me think of lander design. Recent efforts seem to have created a shape that always ends up on its side? XD
Re: A new pyramid-like shape always lands the same side up
#110Earlier 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.
That's like saying a donut only has one side. The linked die seems similar to this: https://cults3d.com/en/3d-model/game/d1-one-sided-die which seems adjacent to a Möbius strip but kinda isn't because the loop is not made of a two sided flat strip. https://wikipedia.org/wiki/M%C3%B6bius_strip Might be an Umbilic torus: https://wikipedia.org/wiki/Umbilic_torus The word side is unclear.
Everyone knows that a donut has two sides.
Inside, and outside.