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

Images and Footage courtesy of Shamini Bundell and Yaroslav Sobolev.

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Creator - Jade Tan-Holmes
Script - Joshua Daniel
Animations - Andrew Brown
3D printing - Stanley Lee

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

[Kaldrin]

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

[dominiklukacs]

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

[johnchessant]

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

[jeremyrixon]

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

[Splarkszter]

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

THANK

[gardenlizard]

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

[silverharloe]

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

[ShawnHCorey]

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.

[GlennHanna]

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.

[jawaduddin]

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]

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

[LetsGetIntoItMedia]

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]

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_]

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]

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

[Nicks]

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!!!)

[vladimir]

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

[mingmerci]

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

[sosanzehra]

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

[iamsushi]

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