"These mathematics were able to show something, noone ever dont before: a mathematical principle demonstrated in the real world." Jokes aside: fun video
I would say, a rolling sand grain on the beach and a rolling small crustacean on the beach due to ocean waves might follow this kind of mathematical theory. Following their moves, we can extrapolate where they will eventually be stranded, deposited and accumulated
Their approaches to Bridgestone, Dunlop, and Goodyear were rudely rebuffed. “Sure you’ve reinvented wheel alignment. But you drove in here like a damn fool son!”
I think you're right: it could be a way to measure the geometry (the convex hull, to be precise). Somehow it didn't occur to me. But I think your idea will work. However, any object rolls in the same way as its convex hull does, so it will be impossible to distinguish a true nonconvex shape from its convex hull just by inspecting its slipless rolling. The trajectoid algorithm calculates the convex hull needed to do the job. In the paper, the shape of each trajectoid is simply this convex hull. And the object must be rolling sliplessly on a slope under action of gravity alone (or some other constant force). I'm afraid, slipless rolling driven by gravity alone is not very common. Planets and nanoparticles (let alone molecules) don't normally roll on a slope, and if they do it's not a slipless solid-body roll. In the case of nanoparticles, for example, electrostatic and Van der Waals forces come into play, as well as diffusion and fluid flows: nanoparticles stick to surfaces, or don't touch them at all.
The way it is easier to trace the pattern twice per rotation, and then the suggestion of a link with quantum mechanics, makes me think of quantum mechanical spin. Maybe there's some deep mathematical reason it works best this way
I would think that a high res resin printer print would be able to produce real life results closer to the computer models as the flaws in the prints produced in the video were clearly visible to the naked eye.
Not exactly the same, but my Nanna rolls down the stairs in similar trajectories. She falls a lot. But she isn't as round as those 3D printed plastic pieces. She is more lumpy.
I see what you mean, but it this specific case this claim is not unfounded. It's shown in the paper that it's so easy to make a two-period trajectoid because, it turns out, almost any finite sequence of 3D rotation matrices whose axes are coplanar can yield the identity matrix when applied twice in a row, if all rotation angles are multiplied by appropriate shared constant. This peculiar property of 3D rotations is directly applicable to the Bloch sphere representation of a qubit. In the context of Bloch sphere, this property means that almost any planar field pulse, once scaled by an appropriate factor and applied twice in a row - will return the quantum system exactly to its original state. You may ask what's the point of performing an action that brings the system back to precisely the same state it was in before this action -- but it's actually one of important operations in pulse sequences used for rotary echo, it's also found in widely-used Wimperis sequences -- see the classical paper at DOI: 10.1006/JMRA.1994.1159 In Wimperis sequences, this operation is done as a single 360-degree rotation. The property found in trajectoids can be directly applied to construct an infinite variety of such identity-matrix-equivalent pulse sequences. It's just a new tool in the pulse sequence designer's toolbox, as I see it.
Each path is infinite, translationally-periodic. And there are infinitely many paths for which a trajectoid exists. But some parts of the associated math are surprizingly deep, who knows when and what will be found once the bottom is reached? Mathematicians should have considered this problem in 23 B.C., not in 2023 A.D.
Since a single path repeats it can roll forever. Since the surface of a sphere has infinitely many points, an infinite non-repeating path should also be possible. Not practical of course, but in theory there should even be infinitely many of those infinite paths.
@@FHBStudioHaving an infinite number of points isn't sufficient for an infinite path. Any (nondegenerate) path already has infinitely many points, but of course not all paths have infinite length. It's still super easy to find examples of infinite curves. Spirals are the easiest to construct for this purpose since hyperbolic and euler spirals can be cut off at a point and the remaining piece have infinite length but occupying a bounded finite-area region. The simplest example for the sphere, however, is a rhumb line, which has a wikipedia entry if you're interested
Thinking about finite vs infinite 1.As time increases the Objects would wear i wonder can you create complete paths that will always wear into other complete paths. 2. Are there complete paths where reversing the slope changes the path en.wikipedia.org/wiki/Sisyphus?wprov=sfla1
I am very disappointed that there isn't a shape that spells out "hello world" when rolling
If you had a shape large enough, then theoretically, you could.
you just dropped a new mathematical challenge
I would pay for that
You could use their algorithm to make a shape that does that, assuming you had the material
Cursive text with a leap?
It'd be cool to make these trace out people's names in cursive.
Can't wait for this to hit table top games.
Ah yes lemme roll the Euler dice
Roll Them Bones!!!
A bakugan-type game with just these
what a brilliant workaround to trace the path twice so it has an easier time to come back to its origin
L pfp
And somehow it reminds me of spinors and how Clifford Algebra describes them.
I wish I could meet people like these researchers. So cool!
This is the solution to so many questions. I love it! ❤
"These mathematics were able to show something, noone ever dont before: a mathematical principle demonstrated in the real world."
Jokes aside: fun video
I would say, a rolling sand grain on the beach and a rolling small crustacean on the beach due to ocean waves might follow this kind of mathematical theory. Following their moves, we can extrapolate where they will eventually be stranded, deposited and accumulated
Not really because here, only slope and gravity are used while in natural environment, you have wind, currents, tidal and plate action, etc.
The butterfly effect exists to disprove this theory.
Their approaches to Bridgestone, Dunlop, and Goodyear were rudely rebuffed. “Sure you’ve reinvented wheel alignment. But you drove in here like a damn fool son!”
Could it be a way to measure the exact geometry of an object (nanoparticules, molecules, planets,...) from the measure of its trajectory ?
I think you're right: it could be a way to measure the geometry (the convex hull, to be precise). Somehow it didn't occur to me. But I think your idea will work. However, any object rolls in the same way as its convex hull does, so it will be impossible to distinguish a true nonconvex shape from its convex hull just by inspecting its slipless rolling. The trajectoid algorithm calculates the convex hull needed to do the job. In the paper, the shape of each trajectoid is simply this convex hull.
And the object must be rolling sliplessly on a slope under action of gravity alone (or some other constant force). I'm afraid, slipless rolling driven by gravity alone is not very common. Planets and nanoparticles (let alone molecules) don't normally roll on a slope, and if they do it's not a slipless solid-body roll. In the case of nanoparticles, for example, electrostatic and Van der Waals forces come into play, as well as diffusion and fluid flows: nanoparticles stick to surfaces, or don't touch them at all.
Do you have an English translation of this?
@@ivanvanogre-nd1sw Translation: those things don't roll the same way.
Gravity + surface to roll on not included here.
Literally The Rolling Stones
The new most convoluted way to leave a secret message
Never thought I’d be so entertained by a rolling object.
wake up babe new mathematics just dropped
Imagine a puzzle game that requires you to create an uneven marble that rolls along a very narrow wavy bridge
wow Shamini Bundell was ON A ROLL in this video
The way it is easier to trace the pattern twice per rotation, and then the suggestion of a link with quantum mechanics, makes me think of quantum mechanical spin. Maybe there's some deep mathematical reason it works best this way
Now dip it in ink and get it to trace out a famous logo, and you'll have yourself a saleable product!
They should find a way to simplify the sides enough to turn them into many-sided dice.
could actually have some potential relevance to other areas of science
This is so freaking awesome
Wallpaper or fabric repeat patterns come to mind..
this needs 3billion more dollars funding every year forever
I would think that a high res resin printer print would be able to produce real life results closer to the computer models as the flaws in the prints produced in the video were clearly visible to the naked eye.
"It was way easier to have it go around twice"
Ohhhhhhhhh now I get the physics link. Cool 😎
I'd like to write Names with this.
This feels relevant to protein folding
I also feel this way but in a way I cant articulate
@@banann_ducc maybe how a polypeptide wraps around a metal ion?
@@Komadaki maybe?? I havent gotten that far into chem yet. (freshman biochem major with a vague idea of what protein folding is from youtube videos)
Thr shaoes seem similar to a Gömböc. (1 stable and 1 unstable point of equilibrium).
Is there any relation?
I had an infestation of Gömböcs in my basement last year. I didn't spot any shaoes though.
Very special
Not exactly the same, but my Nanna rolls down the stairs in similar trajectories. She falls a lot.
But she isn't as round as those 3D printed plastic pieces. She is more lumpy.
I wonder if this can be used to write cursive. Pit some ink on it?
Yup.
These shapes where designed to roll in peculiar ways because they were designed with new mathematics.
Rolling stones gathered by maths :)
Does anybody know how this shapes are called ??
I want to a design one that spells out my name.
Kids invent games. Scientists follow them. Scientific mindset changes a way to contemplate the world. Inspiring, isn't it?
Make it roll uphill= infinite energy glitch
The frick when math got an update?
been updated tons of times recently, got no notifs?
Try this with paths Like Stock market prices
Sculpt coding mayhaps
Can they sculpt code a structure?
Perhaps traverse a maze
Could you roll 100 balls that leave an imprint and be left with a piece of art
Mmh this remember me to the polymer structure, maybe this fan be a mechanic cristal 🤔?
Oh, those silly mathematicians
Super.
Let’s hope it’s put to some practical use
Like ambulance 🚑 dodging traffic
0:07 Why o why, you did not draw a circle?
i want one to trace my name
3:50 I find these kind of claims harmful
Well at least annoying, if not harmful.
I see what you mean, but it this specific case this claim is not unfounded. It's shown in the paper that it's so easy to make a two-period trajectoid because, it turns out, almost any finite sequence of 3D rotation matrices whose axes are coplanar can yield the identity matrix when applied twice in a row, if all rotation angles are multiplied by appropriate shared constant. This peculiar property of 3D rotations is directly applicable to the Bloch sphere representation of a qubit. In the context of Bloch sphere, this property means that almost any planar field pulse, once scaled by an appropriate factor and applied twice in a row - will return the quantum system exactly to its original state. You may ask what's the point of performing an action that brings the system back to precisely the same state it was in before this action -- but it's actually one of important operations in pulse sequences used for rotary echo, it's also found in widely-used Wimperis sequences -- see the classical paper at DOI: 10.1006/JMRA.1994.1159
In Wimperis sequences, this operation is done as a single 360-degree rotation. The property found in trajectoids can be directly applied to construct an infinite variety of such identity-matrix-equivalent pulse sequences. It's just a new tool in the pulse sequence designer's toolbox, as I see it.
@@yaroslavsobolev9514 thank you for pointing this out
Look, everyone inflates the "applications" section of their paper/grant proposal.
@@ShankarSivarajan That doesn't make it right.
"New mathematics" 😂
So what was solved by this.
Thanks to a $100 Million dollar grant from the NSF.
"new mathematics"
So are these peculiar paths finite or infinite? Let’s spend another hundred years to find the answer.😂
Each path is infinite, translationally-periodic. And there are infinitely many paths for which a trajectoid exists.
But some parts of the associated math are surprizingly deep, who knows when and what will be found once the bottom is reached? Mathematicians should have considered this problem in 23 B.C., not in 2023 A.D.
Since a single path repeats it can roll forever. Since the surface of a sphere has infinitely many points, an infinite non-repeating path should also be possible. Not practical of course, but in theory there should even be infinitely many of those infinite paths.
@@FHBStudioHaving an infinite number of points isn't sufficient for an infinite path. Any (nondegenerate) path already has infinitely many points, but of course not all paths have infinite length. It's still super easy to find examples of infinite curves. Spirals are the easiest to construct for this purpose since hyperbolic and euler spirals can be cut off at a point and the remaining piece have infinite length but occupying a bounded finite-area region. The simplest example for the sphere, however, is a rhumb line, which has a wikipedia entry if you're interested
Thinking about finite vs infinite
1.As time increases the Objects would wear i wonder can you create complete paths that will always wear into other complete paths.
2. Are there complete paths where reversing the slope changes the path
en.wikipedia.org/wiki/Sisyphus?wprov=sfla1
interesting!❤
wøw!
With absolutely zero practical uses
not everything has to be useful tbh
There's a possibility it can be used to solve the protein folding problem, a solution essential in finding the cures to cancer.
I think i can use this in my research
Will comeback to this comment after i publish it
Wow 😮 I hate math😂
Next they should make an analog quantum computer with millions of tiny versions of these shapes rolling around inside it
It's pronounced REEsearch, not reSEARCH!
This could be great for encryption, replication of sound wave patterns or to save information on a analog medium, Impressive 🦾🤠👍💯