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You Won’t Believe How These Shapes Roll! New Discovery in Math

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Recommended course: brilliant.org/courses/basic-2...
Trajectoids Nature Article www.nature.com/articles/s4158...
Make your own trajectoid colab.research.google.com/dri...
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Creator - Jade Tan-Holmes
Script - Joshua Daniel
Animations - Andrew Brown
3D printing - Stanley Lee
Music - epidemicsound.com
Chapters:
0:00-0:47 What's a trajectoid?
0:47-1:42 The basic idea
1:42-8:54 Cool math
8:54-10:40 Trajectoid Show-n-Tell
10:40-11:57 Applications of trajectoids

Опубликовано:

10 авг 2024

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Комментарии : 425

@Kaldrin 5 месяцев назад

Math is always about "this looks fun let's try" turning into "wait this is actually very useful"

@pumbaa667 5 месяцев назад

My favourite example are Prime numbers. 2'500 years of research just for the fun of it. And finally a real life usecase appears with asymmetrical encryption ^^

@valiakosilla2413 5 месяцев назад

Not always. If you do not believe me ask from my wife. I have used probably ten thousand hours to all kind of mathematic hobbies with very small useful results.

@aloysiuskurnia7643 5 месяцев назад

I beg to differ! To me maths is about "this looks fun let's try it whether if it is useful or not!" leaving a lot of tools, possibly unuseful at the moment, scattered all around the place. Whether other branches of science accidentally stumble upon our tools and finding it useful is up to them, not us :^)

@sk8rdman 4 месяца назад

Not always. Many mathematical breakthroughs were made in the pursuit of a specific practical goal. I'm sure Newton was a mathematically curious guy, but that alone was not why he invented calculus. He was very interested in understanding planetary motion, and he invented calculus in the pursuit of a rigorous mathematical model that helped explain his observations. It's a similar story with Leibniz. He independently invented his own system of notation for what we now know as calculus, because he needed it to understand and design his calculating machines. It wasn't mere curiosity that motivated these men. They invented calculus because they needed it to solve other (very different) problems that they were working on. The pursuit of mathematical curiosity is great, and it's also great when we find our discoveries have unexpected applications, but it would be a mistake to say that that's how it always does or should work. In fact, understanding the specific sort of problem that motivated a mathematical discovery can often help provide context and intrinsic motivation towards better understanding the math ourselves.

@dominiklukacs7677 5 месяцев назад

"So here is a trajectoid of my heartbeat" *Immediately stops*

@valiakosilla2413 5 месяцев назад

I thought also that I would be somewhat worried if my heart was powered with trajectoid.

@Ath3nx_2 5 месяцев назад

@@valiakosilla2413 same💀

@johnchessant3012 5 месяцев назад

I really like clever ideas like changing from 1 to 2 periods that suddenly makes trajectoids a lot less rare!

@Sau1Bage2-im4mc 5 месяцев назад

Im very much not lying but i had the same idea while watching the video before she said it

@IceMetalPunk 5 месяцев назад

It goes from "infinitely rare" to "guaranteed" just by doubling and rotating. Sometimes math is very cool 😁

@vigilantcosmicpenguin8721 5 месяцев назад

Feels like a hack.

@flameofthephoenix8395 5 месяцев назад

What's most interesting is they said it was infinitely rare then showed that all infinite trajectories have a copy that makes the trajectoids showing that it is at least 50% of all trajectories.

@jeremyrixon150 5 месяцев назад

Hey RU-vid Algorithm! Roll as many lumpy shaped objects as you have in this direction. We want people to follow the lines to UpAndAtom!

@upandatom 5 месяцев назад

@Th3OneWhoWaits 5 месяцев назад

😀

@freddyvejen743 5 месяцев назад

yes we do!

@CMHE 5 месяцев назад

Are you calling me a lumpy shaped object?

@firstname405 5 месяцев назад

@CMHE we are all lumpy shaped objects 💖

@Splarkszter 5 месяцев назад

Woah. You explain soooo well. I love the neat practical examples and everything. THANK YOU!!!!!!!!!!

@upandatom 5 месяцев назад

Thanks!

@gardenlizard1586 5 месяцев назад

So working out the shape of the rock in rock and roll.😊

@silverharloe 5 месяцев назад

10:30 so one could say you really put your heart into this video?

@upandatom 5 месяцев назад

@JasmineLi 4 месяца назад

O-O

@ShawnHCorey 5 месяцев назад

If a trajectoid doesn't complete the path ending in the same orientation, it will repeat the path at a different angle. If that angle is a rational number, it will eventually come back to the initial orientation and then repeat itself. If the angle is an irrational number, it will never repeat itself; the angle of its path will always be different from any before. PS: I should clarify. If the angle measured in degrees is rational, it will eventually repeat itself at the initial orientation. If the angle is measured in radians, then if angle/2π = a/b where a and b are integers, it will eventually repeat itself in the initial orientation. I made this clarification because mathematicians like to measure angles in radians.

@GlennHanna8 5 месяцев назад

I agree with you on not being an expert at something yet being a good explainer by breaking things down. There's a joy in learning and understanding something that seemed difficult at first and then sharing all the parts that made it come together and make sense. Even mentioning the thoughts or ideas that might lead us the wrong way naturally and say "don't think of it that way like I kept doing... think of it this way instead" is very helpful.

@jawaduddin4244 5 месяцев назад

I saw your short on this and wrote an article on my engineering blog about trajectoids a little while back - thank you for bringing this back!

@glennac 5 месяцев назад

LOL! 😂 “Rightway up”. I see what you did with the globe Jade❣️😜

@LetsGetIntoItMedia 5 месяцев назад

I've been looking forward to this one! I remember commenting something about the physical practicalities of these shapes, so it was cool to see you explore those and highlight some issues here! Great video as always, Jade 🤩

@AsianDinner 5 месяцев назад

I've been feeling very stupid lately, but I discovered your videos recently and I love how you present information in such a fun and approachable way. Thank you for your hard work, you deserve the million!

@raman_14264 4 месяца назад

Literally you talent is insane being a teacher, and also sense of humor. Your videos literally make maths a fun subject. Can't wait for your next video

@BooleanDisorder 5 месяцев назад

You have such a vivid and clear way to explain things. Thank you! 😎

@Nicks721 5 месяцев назад

Absolutely incredible, you explain everything very smoothly (unlike the lines of some trajectoids you showed... the trajectoid of the line represanting the smoothness of your explanations will roll forever!!!)

@vladimir10 5 месяцев назад

Awesome vid! Really missed your content, happy to see you again!

@mingmerci6103 5 месяцев назад

I absolutely love this. This made me smile way more than it should

@upandatom 5 месяцев назад

math is wonderful :)

@sosanzehra1227 5 месяцев назад

Jade,I was eagerly waiting for your video and it was such a cool one!

@user-ro9fk7xc9y 2 месяца назад

Sad you stopped making videos.

@iamsushi1056 5 месяцев назад

This new field of physical geometry that’s coming up with things like gombocs and trajectoids is so cool.

@Porcuspine360 Месяц назад

It’s crazy how breedable she is

@JaiMadhusuthan 5 месяцев назад

Really great video as always. You are the best at explaining high level concepts you are my go to person for content like this!

@MemphiStig 4 месяца назад

I always enjoy you explaining stuff and introducing me to things I've never heard of. Your videos are always well done, informative and fun.

@dj_laundry_list 5 месяцев назад

What if I said that the Fourier transform decomposes a hilbert space into orthogonal basis vectors?

@tagbon 5 месяцев назад

Great video. Always fun and educational - thanks! 🥰

@ShaneH42 5 месяцев назад

Geometry makes my brain not want to brain but your demos really helped. Great video

@debtanaysarkar9744 5 месяцев назад

Yayyyy, you're back again, awesome video once again

@gameon6252 5 месяцев назад

Thank God you had stan with you jade , he is the MVP. Was always excited to know about trajectoids thanks Jade🎉

@Hossak 5 месяцев назад

Hitting it out of the park as usual. Nice work Jade!!!

@me0101001000 5 месяцев назад

I see this having interesting applications in materials science, too. There are lots of people in materials science who work on something called "Advanced Materials", which involves creating new materials from existing ones which have incredible new properties. I can see these trajectoids being used to inspire or even create new crystal coordinations with very interesting structures and properties. I'm excited to see this eventually trickle into my field!

@gazman1238 5 месяцев назад

Really fascinating. Thanks for the vid. These trajectoids seen to relate to a sphere the way a cam relates to a circle.

@aianyoung 5 месяцев назад

Thank you for continuing to make excellent videos on complex subjects in an easily digestible way. I've greatly enjoyed watching your channel for the past few years!

@GermanSausagesAreTheWurst 5 месяцев назад

Your videos just keep getting better and better. I am in awe of not only your mathematical ability, but also your video production.

@cogwheel42 5 месяцев назад

5:30 - Yes, I actually did! You did such a good job introducing the topic I anticipated the punch line :)

@stephenpuryear 5 месяцев назад

Jade I am so glad that you have persisted in making these videos. I also really love the background that you frequently shoot in front of. That particular shade of blue is soothing but also eye catching, along withe the formulas on the black placards Lastly, I am convinced that as a species, we need to keep descending deeper into three or more dimensions as we seek "explanations" for how our world really works. Thanks for these videos!

@abdul-kabiralegbe5660 5 месяцев назад

I'm happy to see this channel grow. Over 700k!

@AbdullahCumhur 5 месяцев назад

I once saw your short video about this topic and I tried to recreate it myself but it didn't work, so after watching this video I'll try again lol

@adamengelhart5159 5 месяцев назад

This is the most fun math thing I've seen since the monotile from last year! Thanks!

@piyush197sharma 2 месяца назад

I am following this channel for 2 years and realised that it was very brilliant part for me she cleared my all doubts about quantum physics and quantum biology thank you very very much

@alex4833 5 месяцев назад

This is neat :). I was intrigued throughout and am interested in Brilliant's courses. Awesome video! Have a marvelous week, Jade! :). Take care.

@Watchmedothatfor.u 5 месяцев назад

I found this channel yesterday and i already love it ! Go physics,math and astronomy ❤❤🎉🎉

@powertomato 5 месяцев назад

I started following this channel because I noticed familiar topics from my university classes and on each one I was thinking "I wish my professor was this good at explaining it". I really think this kind of breaking things up to its most basic concepts opens it up to a much broader audience and leads to a deeper understanding. Math and logic in school are often very dry and driven by purpose. That's like teaching art to learn brush techniques, but never stopping to appreciate how beautiful the paintings are. Thanks for showing the beautiful side of math.

@vitaminluke5597 5 месяцев назад

"Trajectoid" sounds like an overly specific online political insult.

@rpow6861 5 месяцев назад

all this kinda stuff is so damn cool!! i haven't got a clue about any of it but that doesn't stop me from loving it!!

@JoshtMoody 5 месяцев назад

This is freaking fantastic. Thank you so much for making this video. When I watched this I was instantly reminded of the WW2 'mechanical computers' to get pretty accurate shelling. This is taking it up a level though. I love it. I am going to try to make one of these things to make a mechanical computer to model levitation of liquid rubidium in vacuum. I can cross-reference to some FEM modelling in COMSOL and then have some decent confidence in my prototype before I assemble and test it. Thanks again I am so jazzed.

@pluggedingaming8169 5 месяцев назад

Having two periods, the same pattern mirrored on each side of the ball, it equally splits it perfectly in half and ensures that the path you want is still followed.

@user-tc9qy8hv4n 5 месяцев назад

Great video 😊 you make learning more fun.

@bungkiukissinquinker7563 5 месяцев назад

I was missing this lady's videos for a few days now. Happy to learn new stuffs again from her.

@orterves 5 месяцев назад

Everything about this is awesome

@punditgi 5 месяцев назад

Jade is back and totally awesome! ❤🎉😊

@kjh23gk 5 месяцев назад

You explained this brilliantly!

@upandatom 5 месяцев назад

thank you!

@puffinjuice 5 месяцев назад

I like how you demonstrated the ideas with a ball and clay snake. Clever!

@kam1470 5 месяцев назад

I see Jade, i watch! :D Congrats on 714K Subs. Its been 500K the last time i congratulated, so you went a long way in short period of time.

@pisscow6395 5 месяцев назад

Such a cool video! I struggle a lot in understanding math and physics but this was so well explained and entertaining!

@matteogiberti3297 5 месяцев назад

As usual... Amazing video and Amazing Jade!

@algorithminc.8850 5 месяцев назад

A really fun one ... thanks ... Cheers ...

@mohammadrezamoalemnia9201 5 месяцев назад

I always learn from you and I love that!

@ofgaut 4 месяца назад

Such a great and easy to understand explanation.

@christoforusbayurisanto1793 4 месяца назад

Very insightful! Thank you

@LarkyLuna 5 месяцев назад

This feels like a Fourier series but you're embedding the periods into a sphere instead of a complex circle I wonder if you can relate the two in any way or reduce fourier into a special case of trajectoids Very interesting math!

@DerpMuse 4 месяца назад

Not quite fourier. These trajectoids have an identity of 4pi.

@faisalsheikh7846 5 месяцев назад

Plz make a video on Godel Incompleteness theorem

@mimetype 5 месяцев назад

Isn't it incomplete?

@NamanNahata-zx1xz 5 месяцев назад

@@mimetype You did not just

@mimetype 5 месяцев назад

@@NamanNahata-zx1xz Sorry :)

@captainchaos3667 5 месяцев назад

Love the animations in this. Must have been a challenge.

@drunkuchiwa9361 5 месяцев назад

Great video !!!!!!!!!🙌

@Mrkino 5 месяцев назад

Thanks for another great video!

@aniksamiurrahman6365 5 месяцев назад

Now I have a new challenge to these mathematicians - discover at least one trajectoid solid whoich traces a completely aperiodic path.

@benjaminwood8736 5 месяцев назад

Not possible (I don’t think) because the shape would need an infinite number of sides, if it had a finite number of sides, when you push the shape from on face to another from the same direction, it always goes to the same next face (otherwise it wouldn’t make periodic things either), since pushing from each face in every direction leads to limited options, it means that eventually you would have do the same thing twice, I think the total number of options is somewhere in the ballpark of ((number of faces attacked to current face) * (number of faces)!)

@benjaminwood8736 5 месяцев назад

Actually thinking a bit more it should be around (the sum of ((the number of attached faces to current face) * (number of faces)!) for each face)

@aniksamiurrahman6365 5 месяцев назад

@@benjaminwood8736 May be. On a second watch, a different question came to my mind. The mechanics of real world trajectoids should also be studied. Like, how their mass, volume, the driving force, and the smoothness of the surface relate to mobility. That may not be that costly of a research either. But a quite laborious one. I think I shud post this reply too as a OP comment.

@MrHerhor67 5 месяцев назад

Like, a ball?

@benjaminwood8736 5 месяцев назад

@@MrHerhor67 A ball makes a straight line, the force put on the trajectoid doesn't change

@jakubr2769 5 месяцев назад

0:07 LITTLE PRINCE!

@davidgillies620 5 месяцев назад

I saw this and immediately thought "parallel transport and spinors" and lo and behold, up pops the Bloch sphere. The angle doubling as applied to qubits is a dead giveaway. You see that everywhere, from light polarisation to quantum spin states.

@mikhailgastby4680 5 месяцев назад

Fantastic. This shape made a new view to represent 3d objects and formal actions , great vídeo, and you run infinal vídeo Jade ? Hahahaja

@freddyjosereginomontalvo4667 5 месяцев назад

Awesome videos as always say 🌍🌟 You are awesome ❤ Take care

@bejoscha 5 месяцев назад

As usual, a really well made video with nice and insightful illustrations, just the right speed and joyful presentation. And a cool topic of course as well. (One lost opportunity: Making a joke of needing a pacemaker for the heartbeat trajectoid.)

@kenjinks5465 5 месяцев назад

When tiling a plane, you can start with a square lattice and manipulate the boundaries of one cell to create different shapes that tile the plane. If you start with a sphere with an equator, you can design a path so that when you apply your shape half way around the equator, and the inverse of the shape on the other half of the equator, the two halves will always have the same area. So, this is a tiling on a sphere problem, but you only get two tiles on the sphere. I wonder if it can be broadened and start with three equators at 90deg to each other, and apply the manipulation to the edges and constrain the eight faces to have the same area, what properties that object may have. Since the ball now needs to rotate less than 180deg to produce one period, the period I would theorize to be more stable.

@chad6849 5 месяцев назад

Most underrated channel on YT. Note: due to content not because my daughter is named Jade as well.

@upandatom 5 месяцев назад

@vortonu3155 5 месяцев назад

In honor of the discovery, I will end this sentence with two periods..

@dhonantarogundul1737 5 месяцев назад

Since Fourier Transform is also closely related to periodic things, I wonder if there is some kind of homomorphism going on between the trajectoid and the Fourier Transform.

@dkloke 5 месяцев назад

Heartbeat trajectoid is very cool, props to Stan! Has anyone thought about and tried having hollow trajectoids with one or more weighted balls (or trajectoids?) on the inside to gather and release the weight to overcome at least small loops and abrupt turns? These would have to be tuned for specific inclines and initial velocities. The path for the internal weights might have to be a tunnel, the path moving closer to the center then dropping towards the surface to give the kinetic kick to overcome the difficult transition. But not hard to realize with a 3D printer, although the inner weight (small ball bearing?) might have to be placed into the trajectoid during a pause in the printing process. Thank you for the video!

@ramonhamm3885 5 месяцев назад

Fascinating!

@szboid 5 месяцев назад

Thanks Jade, It brightens my day and my mind when I watch one of your videos.

@upandatom 5 месяцев назад

Wow, thank you!

@Lladra 5 месяцев назад

Cool! thanks

@FlipFlopMLBB 5 месяцев назад

I like how the papers in her background changed orders

@mikchrungBLADES 3 месяца назад

Jade, your videos are all easy to understand and relate to, and beautiful just like you.

@spd4133 5 месяцев назад

Wow it presents a fascinating theory

@Paddymadeathing 5 месяцев назад

Reminds me of a sphericons which Maker's Muse (@MakersMuse) did a video on in a similar vain - modifications of solids in a wawy to create shapes that will roll smoothly along a none straight path

@robertsmith4129 4 месяца назад

This is fascinating to me. I’ve studied a lot of math but have never really considered this concept.

@HiggsBosonandtheStrangeCharm 5 месяцев назад

....i had no interest in trojectoids until Jade presented them in this video.....she is such a great presenter.....such a pleasant voice......so bright.....i've fallen in love......with trojectoids that is........thank you Jade for making such wonderful videos......

@SaiGanesh314 5 месяцев назад

Can't really express how much I'm in love with this! I study at the Universitetet i Agder (UiA) in Norway and I think we have a 3D printer lying around somewhere in our Mechatronics Lab... now I want a trajectoid of my heartbeat and body silhouette drawn on the boundary xD 😂 Thanks for spreading your infectious passion for math into me. 3B1B and you have been strong forces for me to tinker about mathy-silly things that i daydream about ✨️ 💞

@bradycall1889 5 месяцев назад

So cool!

@yaa40 5 месяцев назад

I'm been subscribed to you channel for who knows how long. This is the first time I realized - you have a jumping eyebrow! It's awesome. Oh, and your videos are great too :D

@Impatient_Ape 5 месяцев назад

So which set of orthogonal basis functions do you use to decompose the closed paths on the sphere? Is it still sines and cosines (Fourier)? Is it Legendre polynomials?

@chadjones1266 5 месяцев назад

Thanks again

@ornithopterindia 5 месяцев назад

👍Thank you Madam.

@marcfruchtman9473 5 месяцев назад

Interesting. Thanks for mentioning the Bloch Sphere.

@MathIndy 5 месяцев назад

An electron requires 720 degrees to complete a single rotation. The two cycles of the trajectoid made me wonder if there is any mathematical connection between the two.

@marcfruchtman9473 5 месяцев назад

@@MathIndyYes! Unfortunately, I am not a math head... I am sure Bohr could probably hash out the math. It might also just be that they share they same problem geometrically. And the quantum state is somehow related in that way... ( I have been trying to piece things together conceptually tho, and the 720 degrees relationship was very striking).

@n0madIPX 5 месяцев назад

Wow enjoying the new clear mic

@DhammaBOY 4 месяца назад

Loved your videos

@maxwellhavoc6996 5 месяцев назад

I can’t wait to try this for myself. I have a 3D printer too

@armanavagyan1876 5 месяцев назад

Pretty interesting 👍

@albertandearthie7138 8 дней назад

this channel answers questions nobody asked but everyone needs so well it's only second to Vsauce

@LeeCanPotato 5 месяцев назад

I look forward to signing things by rolling my own unique ball covered in ink.

@Amethyst_Friend 5 месяцев назад

The famous raised eyebrow of curiosity. Thanks Jade

@Thiesi 5 месяцев назад

10:10 - Ugh, until that point in the video I was _absolutely sure_ I had heard about those thargoids before but couldn't actually put my finger on _where._ Well, it makes sense it would have been on a RU-vid channel that exclusively focuses on such stuff, so thanks for solving that mystery for me.