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

Рет қаралды 231,195

Күн бұрын

Sign up to Brilliant to receive a 30-day free trial + a 20% discount with this link! brilliant.org/...
Recommended course: brilliant.org/...
Trajectoids Nature Article www.nature.com...
Make your own trajectoid colab.research...
Images and Footage courtesy of Shamini Bundell and Yaroslav Sobolev.
Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :)
/ upandatom
Visit the Up and Atom store
store.nebula.a...
Subscribe to Up and Atom for physics, math and computer science videos
/ upandatom
For a one time donation, head over to my PayPal :) www.paypal.me/...
A big thank you to my AMAZING PATRONS!
Jonathan Koppelman, Michael Seydel, Cy 'kkm' K'Nelson, Thorsten Auth, Chris Flynn, Tim Barnard, Izzy Ca, Tate Lyles, Richard O McEwen Jr, Scott Ready, John H. Austin, Jr., Brian Wilkins, David Johnston, Thomas Krause, Lynn Shackelford, Ave Eva Thornton, Andrew Pann, Anne Tan, Jeffrey Dutt, Joseph Lamoree, Francisco, Marc-Antoine, Chris Davis, Thomas Urech, chuck zegar, David Tuman, Ben Mitchell, Tyler Simms, James Mahoney, Jim Felich, Fabio Manzini, Jeremy, Sam Richardson, Robin High, KiYun Roe, DONALD McLeod, Ron Hochsprung, Aria Bend, James Matheson, Kevin Anderson, Alexander230, Tim Ludwig, Alexander Del Toro Barba, Justin Smith, A. Duncan, Mark Littlehale, Tony T Flores, Dagmawi Elehu, Jeffrey Smith, Alex Hackman, bpatb, Joel Becane, Paul Barclay, 12tone, John Lakeman, Jana Christine Saout, Jeff Schwarz, Yana Chernobilsky, Louis Mashado, Michael Dean, Chris Amaris, Matt G, Dag-Erling Smørgrav, John Shioli, Todd Loreman, Susan Jones, Bryan Andre, Miles Freeman, Bunny Lushington, JRM, Motty Porat, Michael Tardibuono, Yaw Mintah, Carlos Escolar, Anthony Docimo, robert lalonde, Julian Nagel, Cassandra Durnord, Antony Birch, Paul Bunbury, David Shlapak, Kent Arimura, Phillip Rhodes, Michael Nugent, James N Smith, Roland Gibson, Piotr Klos, Joe McTee, Oleg Dats, John Spalding, Simon J. Dodd, Tang Chun, Michelle, William Toffey, Michel Speiser, James Horsley, Brian Williams, Craig Tumblison, Cameron Tacklind, 之元丁, Kevin Chi, Lance Ahmu, Markus Lindström, Steve Watson, Midnight Skeptic, Potch, Thomas P Taft, Indrajeet Sagar, Markus Herrmann, Gil Chesterton, Alipasha Sadri, Pablo de Caffe, Colin Byrne, Nick H, Jesper de Jong, Sofia Fredriksson, Phat Hoang, Spuddy, Sascha Bohemia, tesseract, Stephen Britt, KG, Hansjuerg Widmer, John Sigwald, O C, Carlos Gonzalez, Thomas Kägi, James Palermo, Chris Teubert, Fran, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Louis M, ROBERT C PAYNE, Moose Thompson, Rick DeWitt, Pedro Paulo Vezza Campos, S, Garrett Chomka, Rebecca Lashua, Pat Gunn, George Fletcher, RobF, Vincent Seguin, Michael Brunolli, Shawn, Israel Shirk, Jesse Clark, Steven Wheeler, Philip Freeman, Armin Quast, Jareth Arnold, Simon Barker, Lou, amcnea and Simon Dargaville.
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

Пікірлер: 426

@Kaldrin 5 ай бұрын

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

@pumbaa667 5 ай бұрын

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 ай бұрын

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 ай бұрын

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 5 ай бұрын

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.

@johnchessant3012 5 ай бұрын

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

@Sau1Bage2-im4mc 5 ай бұрын

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

@IceMetalPunk 5 ай бұрын

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

@vigilantcosmicpenguin8721 5 ай бұрын

Feels like a hack.

@flameofthephoenix8395 5 ай бұрын

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.

@dominiklukacs7677 5 ай бұрын

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

@valiakosilla2413 5 ай бұрын

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

@Ath3nx_2 5 ай бұрын

@@valiakosilla2413 same💀

@jeremyrixon150 5 ай бұрын

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

@upandatom 5 ай бұрын

@Th3OneWhoWaits 5 ай бұрын

😀

@freddyvejen743 5 ай бұрын

yes we do!

@CMHE 5 ай бұрын

Are you calling me a lumpy shaped object?

@firstname405 5 ай бұрын

@CMHE we are all lumpy shaped objects 💖

@Splarkszter 5 ай бұрын

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

@upandatom 5 ай бұрын

Thanks!

@GlennHanna8 5 ай бұрын

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.

@gardenlizard1586 5 ай бұрын

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

@silverharloe 5 ай бұрын

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

@upandatom 5 ай бұрын

@JasmineLi 4 ай бұрын

O-O

@glennac 5 ай бұрын

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

@ShawnHCorey 5 ай бұрын

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.

@jawaduddin4244 5 ай бұрын

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!

@dj_laundry_list 5 ай бұрын

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

@mingmerci6103 5 ай бұрын

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

@upandatom 5 ай бұрын

math is wonderful :)

@iamsushi1056 5 ай бұрын

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

@Porcuspine360 2 ай бұрын

It’s crazy how breedable she is

@raman_14264 4 ай бұрын

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

@ShaneH42 5 ай бұрын

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

@Nicks721 5 ай бұрын

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!!!)

@LetsGetIntoItMedia 5 ай бұрын

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 ай бұрын

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!

@me0101001000 5 ай бұрын

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!

@user-ro9fk7xc9y 2 ай бұрын

Sad you stopped making videos.

@aniksamiurrahman6365 5 ай бұрын

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

@benjaminwood8736 5 ай бұрын

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 ай бұрын

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 ай бұрын

@@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 ай бұрын

Like, a ball?

@benjaminwood8736 5 ай бұрын

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

@BooleanDisorder 5 ай бұрын

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

@piyush197sharma 2 ай бұрын

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

@pluggedingaming8169 5 ай бұрын

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.

@AbdullahCumhur 5 ай бұрын

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

@debtanaysarkar9744 5 ай бұрын

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

@MemphiStig 5 ай бұрын

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.

@rpow6861 5 ай бұрын

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!!

@cogwheel42 5 ай бұрын

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

@JoshtMoody 5 ай бұрын

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.

@GermanSausagesAreTheWurst 5 ай бұрын

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

@aianyoung 5 ай бұрын

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!

@abdul-kabiralegbe5660 5 ай бұрын

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

@gameon6252 5 ай бұрын

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

@LarkyLuna 5 ай бұрын

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 ай бұрын

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

@adamengelhart5159 5 ай бұрын

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

@vortonu3155 5 ай бұрын

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

@faisalsheikh7846 5 ай бұрын

Plz make a video on Godel Incompleteness theorem

@mimetype 5 ай бұрын

Isn't it incomplete?

@NamanNahata-zx1xz 5 ай бұрын

@@mimetype You did not just

@mimetype 5 ай бұрын

@@NamanNahata-zx1xz Sorry :)

@vitaminluke5597 5 ай бұрын

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

@kenjinks5465 5 ай бұрын

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.

@powertomato 5 ай бұрын

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.

@AndTecks 5 ай бұрын

my trajectoid landed me in jail :(

@AlperenBozkurt-tx2bx 5 ай бұрын

How

@Shaynes73 5 ай бұрын

So sorry

@AndTecks 5 ай бұрын

lets just say, daddy Icarus flew too close to the sun. Don't make the same mistakes as me.

@AndTecks 5 ай бұрын

@@AlperenBozkurt-tx2bx 42

@AndTecks 5 ай бұрын

@@Shaynes73 ty love

@punditgi 5 ай бұрын

Jade is back and totally awesome! ❤🎉😊

@stephenpuryear 5 ай бұрын

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!

@kjh23gk 5 ай бұрын

You explained this brilliantly!

@upandatom 5 ай бұрын

thank you!

@tagbon 5 ай бұрын

Great video. Always fun and educational - thanks! 🥰

@orterves 5 ай бұрын

Everything about this is awesome

@Impatient_Ape 5 ай бұрын

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?

@jakubr2769 5 ай бұрын

0:07 LITTLE PRINCE!

@dhonantarogundul1737 5 ай бұрын

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.

@davidgillies620 5 ай бұрын

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.

@Watchmedothatfor.u 5 ай бұрын

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

@puffinjuice 5 ай бұрын

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

@bungkiukissinquinker7563 5 ай бұрын

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

@FlipFlopMLBB 5 ай бұрын

I like how the papers in her background changed orders

@vladimir10 5 ай бұрын

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

@alex4833 5 ай бұрын

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

@szboid 5 ай бұрын

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

@upandatom 5 ай бұрын

Wow, thank you!

@chad6849 5 ай бұрын

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

@upandatom 5 ай бұрын

@marcfruchtman9473 5 ай бұрын

Interesting. Thanks for mentioning the Bloch Sphere.

@MathIndy 5 ай бұрын

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 ай бұрын

@@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).

@ofgaut 4 ай бұрын

Such a great and easy to understand explanation.

@LeeCanPotato 5 ай бұрын

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

@gazman1238 5 ай бұрын

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

@drunkuchiwa9361 5 ай бұрын

Great video !!!!!!!!!🙌

@sosanzehra1227 5 ай бұрын

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

@JaiMadhusuthan 5 ай бұрын

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

@raffimolero64 5 ай бұрын

You know it's a great explanation when it leaves you feeling like you could've discovered it yourself.

@Hossak 5 ай бұрын

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

@user-tc9qy8hv4n 5 ай бұрын

Great video 😊 you make learning more fun.

@anthonycarbone3826 5 ай бұрын

This sounds like it is a variation of the bezier curve mathematics.

@pisscow6395 5 ай бұрын

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

@albertandearthie7138 12 күн бұрын

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

@fnx427 5 ай бұрын

Should've named them "Pathtatoes".

@Amethyst_Friend 5 ай бұрын

The famous raised eyebrow of curiosity. Thanks Jade

@robertsmith4129 4 ай бұрын

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

@dkloke 5 ай бұрын

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!

@EyesOfByes 5 ай бұрын

5:44 No way they did that *Le Petit Prince* reference!! That's the most adorable meme I've ever seen!

@vigilantcosmicpenguin8721 5 ай бұрын

I just think it's rude to the elephant to roll that shape over it so many times. But probably not as rude as digesting it as an anaconda.

@tylerbakeman 5 ай бұрын

What do you think about the surface forming a closed loop at any point along the surface- if that’s even possible

@matthewhafner962 5 ай бұрын

When you got to the 2 period part, I went "oh yeah, antimatter." If you rotate a particle only 360 degrees, you get it's antiparticle. You have to rotate it 720 degrees to get the same particle again.

@mikhailgastby4680 5 ай бұрын

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

@maxwellhavoc6996 5 ай бұрын

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

@martindorrance8133 5 ай бұрын

Hi Jade. Could the 2-cycle pattern be analogous to electron spin in any way?

@MathIndy 5 ай бұрын

This occurred to me as well.

@Attemptedburger 5 ай бұрын

this reminds me of gears and cams, but sideways instead of up and down

@Paddymadeathing 5 ай бұрын

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

@bejoscha 5 ай бұрын

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.)

@realsushrey 5 ай бұрын

Phds in physics be like: I am not very mathematically minded.

@merijein9418 5 ай бұрын

having a shape that can imitate EVERY line a person can draw is actually damn amazing. I love math, but my little peanut brain can just look at it and say "WOW!"

@christoforusbayurisanto1793 4 ай бұрын

Very insightful! Thank you

@Geopholus 5 ай бұрын

I am quite sure that this inquiry into trajectoids, has an absolutely MIND BOGGLING & universal application to helping explain /( prove ?) not only that string theory fits with TOE, but how electron "paths" result in constructively reinforcing standing waves (which result in fundamental particles), . I have done lots of experiments with what I call the "baseball curve" the shape of the two flaps of leather (equal in size) that are used to cover a baseball, and now see that the 2 pi R 180 degree rotation trajetoids also fulfill the property, of tracing a path around a sphere, that when translated by the trajectory of it's own outline, end up equally distributing coverage of the sphere,... (hence a stable standing wave)

@brromo 5 ай бұрын

The straight line trajectoid is a cylinder. The circle trajectoid is a cone

@spd4133 5 ай бұрын

Wow it presents a fascinating theory

@kam1470 5 ай бұрын

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.

@SaiGanesh314 5 ай бұрын

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 ✨️ 💞

@DeclanMBrennan 5 ай бұрын

Great explanation with some beautiful graphics. To keep the trajectoid on track, how about putting some teeth on both it and the surface that it is rolling on to create some really funky gears? The teeth should be at right angles to the intended motion and very sharp turns might still be an issue. Ultimately the surface being rolled could be a second trajectoid. I'll leave the maths as an exercise. :-)

@AdityaSharma-th1gl 5 ай бұрын

Beauty with Brain😊 A very rare combination

@mikchrungBLADES 3 ай бұрын

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

@AgentOccam 5 ай бұрын

You could do a whole video on the qubits/quantum physics aspect. What exactly IS a qubit? What is it to exist in a "mix" of states? (That, and "Spooky action at a distance" are the two most confounding things in quantum physics.)

@BallotBoxer 5 ай бұрын

Could be useful for a funky lock: roll the right trajectoid to trace the correct path to unlock the door.

@reddcube 5 ай бұрын

If you wanted the 2 periods of your rolling path to be mirrors of each other, could you reflect the path across the great arc instead of rotating it? Or would you need to making a ball that uses 4 periods.