I am very disappointed that there isn't a shape that spells out "hello world" when rolling

@whobitmyneck

10 ай бұрын

If you had a shape large enough, then theoretically, you could.

@___-qj2lx

10 ай бұрын

you just dropped a new mathematical challenge

@kamikeserpentail3778

10 ай бұрын

I would pay for that

@mr.theking2484

9 ай бұрын

You could use their algorithm to make a shape that does that, assuming you had the material

@CONNELL19511216

8 ай бұрын

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.

@Mordecrox

10 ай бұрын

Ah yes lemme roll the Euler dice

@ivanvanogre-nd1sw

10 ай бұрын

Roll Them Bones!!!

@officersoulknight6321

10 ай бұрын

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

@zeppie_

9 ай бұрын

L pfp

@aniksamiurrahman6365

9 ай бұрын

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

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!”

The new most convoluted way to leave a secret message

wake up babe new mathematics just dropped

Never thought I’d be so entertained by a rolling object.

Could it be a way to measure the exact geometry of an object (nanoparticules, molecules, planets,...) from the measure of its trajectory ?

@yaroslavsobolev9514

11 ай бұрын

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.

@ivanvanogre-nd1sw

10 ай бұрын

Do you have an English translation of this?

@maryamkhan7953

10 ай бұрын

​@@ivanvanogre-nd1sw Translation: those things don't roll the same way. Gravity + surface to roll on not included here.

Literally The Rolling Stones

Now dip it in ink and get it to trace out a famous logo, and you'll have yourself a saleable product!

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

@maryamkhan7953

10 ай бұрын

Not really because here, only slope and gravity are used while in natural environment, you have wind, currents, tidal and plate action, etc.

@unliving_ball_of_gas

9 ай бұрын

The butterfly effect exists to disprove this theory.

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

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

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

Wallpaper or fabric repeat patterns come to mind..

This is so freaking awesome

this needs 3billion more dollars funding every year forever

Thr shaoes seem similar to a Gömböc. (1 stable and 1 unstable point of equilibrium). Is there any relation?

@snufflehound

10 ай бұрын

I had an infestation of Gömböcs in my basement last year. I didn't spot any shaoes though.

I'd like to write Names with this.

"It was way easier to have it go around twice" Ohhhhhhhhh now I get the physics link. Cool 😎

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.

I wonder if this can be used to write cursive. Pit some ink on it?

@maryamkhan7953

10 ай бұрын

Yup.

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.

Rolling stones gathered by maths :)

Does anybody know how this shapes are called ??

Mmh this remember me to the polymer structure, maybe this fan be a mechanic cristal 🤔?

Try this with paths Like Stock market prices

This feels relevant to protein folding

@banann_ducc

10 ай бұрын

I also feel this way but in a way I cant articulate

@Komadaki

10 ай бұрын

@@banann_ducc maybe how a polypeptide wraps around a metal ion?

@banann_ducc

10 ай бұрын

@@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)

I want to a design one that spells out my name.

Make it roll uphill= infinite energy glitch

interesting!❤

These shapes where designed to roll in peculiar ways because they were designed with new mathematics.

Super. Let’s hope it’s put to some practical use Like ambulance 🚑 dodging traffic

Sculpt coding mayhaps Can they sculpt code a structure? Perhaps traverse a maze

@Austinn72

11 ай бұрын

Could you roll 100 balls that leave an imprint and be left with a piece of art

The frick when math got an update?

@molybd3num823

10 ай бұрын

been updated tons of times recently, got no notifs?

Oh, those silly mathematicians

Kids invent games. Scientists follow them. Scientific mindset changes a way to contemplate the world. Inspiring, isn't it?

i want one to trace my name

"New mathematics" 😂

Next they should make an analog quantum computer with millions of tiny versions of these shapes rolling around inside it

So are these peculiar paths finite or infinite? Let’s spend another hundred years to find the answer.😂

@yaroslavsobolev9514

11 ай бұрын

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.

@FHBStudio

11 ай бұрын

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.

@SilverLining1

11 ай бұрын

​@@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

@wakelamp

10 ай бұрын

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

Thanks to a $100 Million dollar grant from the NSF.

So what was solved by this.

wøw!

"new mathematics"

3:50 I find these kind of claims harmful

@user255

11 ай бұрын

Well at least annoying, if not harmful.

@yaroslavsobolev9514

11 ай бұрын

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.

@toxicore1190

11 ай бұрын

@@yaroslavsobolev9514 thank you for pointing this out

@ShankarSivarajan

10 ай бұрын

Look, everyone inflates the "applications" section of their paper/grant proposal.

@user255

10 ай бұрын

@@ShankarSivarajan That doesn't make it right.

0:07 Why o why, you did not draw a circle?

Wow 😮 I hate math😂

With absolutely zero practical uses

@molybd3num823

10 ай бұрын

not everything has to be useful tbh

@jinminetics599

9 ай бұрын

There's a possibility it can be used to solve the protein folding problem, a solution essential in finding the cures to cancer.

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 🦾🤠👍💯