Square Wheels - Reinventing the Wheel
How can a tricycle with square wheels roll smoothly? Join me as we see one in action and learn the math behind it.
Thanks to the team at MoMath for all the help! Check them out at momath.org/
Sections:
0:00 Tricycle
0:48 Constraints
2:43 Setting up equation
4:52 Solving
5:34 Proof of integral
5:42 Conclusion
6:25 Catenary
Пікірлер: 23
Was looking forward to this one, very clearly explained! I'll be forwarding this video to visitors who are interested in the exhibit in the future.
@mostly_mental
3 жыл бұрын
I'm glad you liked it.
Only through the tricycle in real life did I suddenly come to the realization that it’s like the floor and the circular tire just switched places geometrically. I just started the video and I don’t know if you mentioned this in the video, but I had to say it. This is a very cool channel, already subscribed.
@mostly_mental
Жыл бұрын
Glad you like it. Thanks for watching!
New sub here! Wonderful video, liked the channel's theme in general. I'm into pure maths and interesting stuff and this was a lucid explanation. Nice videography, keep it coming!
@mostly_mental
2 жыл бұрын
Thanks! Glad you liked it.
Good explanation, simple approach. Nice!
@mostly_mental
Ай бұрын
Glad you liked it. Thanks for watching!
Nice explanation!
Just fantastic. Intriguing topic.
@mostly_mental
2 жыл бұрын
Thanks! Glad you liked it.
Subscribed!
Nice video learnt a lot!
@mostly_mental
2 жыл бұрын
Thanks! Glad you liked it.
Nice
Wow
Which camera are u using to record your board?
@mostly_mental
2 жыл бұрын
Just my phone. I've got a camera mount that lets me take video from above.
can we know what size must the surface of the part of circle be on order for the wheel to go on smoothly? if i have a wheel that its side is 2 meters for example what should the lengh of the part of the circle be ?
@mostly_mental
Жыл бұрын
The wheel rolls without slipping, so the length of the path needs to be the same as the length of the side of the wheel (in this case 2 meters). You can think of breaking the wheel into lots of very tiny segments and laying each along the curve where that part of the wheel touches the ground. (Also, it's not a circle, it's a hyperbolic cosine.)
How to measure the curve of the road ?
@mostly_mental
2 ай бұрын
If you want to measure the length, the easiest way is to notice that the length of each arc of the curve must be the same as the length of one side of the square (which is 2). If you want to know how curved it is, the best measure is the radius of curvature, which essentially finds the radius of circle that best approximates the curve at each point. There's a formula here en.wikipedia.org/wiki/Radius_of_curvature (which comes out to cosh(x + c)^2).
YOOOOOO