Shortest path? Just unroll the cylinder!

We have two points on a cylinder's curved surface, one inside and the other outside. How can we find the shortest path between the two points?

To do that, watch how we can transform the cylinder into a simpler shape and use the idea of symmetry.

Puzzles like these help build mathematical thinking and logical reasoning skills.
Learn math the Cuemath way. Click the link on the homepage.

#math #education #learning #puzzle #reasoning #cylinder #rectangle #symmetry

[luckytrinh]

The ant 🐜 taking out it's laptop to implement dijkstra's algorithm real quick 😎

[Alam_Khan]

The first thing that came to my mind is it should follow the path of reflection

[devang]

As a lawyer of ants - if we find a drop of honey we don't just start calculating the shortest path...

[soumyamahapatra]

Did he just taught Geodesic in riemannian manifold so simply??? Just excellent

[jffrysith]

Im not sure if this is still true, because the surface is curved, walking around the ouside is ever so slightly longer than the inside. This means that the ant should ever so slightly prioritise getting into the cylinder meaning the optimal path would be ever so slightly angled away from the honey at first and then a straight line from the purple line to the honey.

Do note this is very insignificant, but its an interesting factor to consider and a reason why simple (unproven) visual explanations can miss interesting factors.

(Also this is still true on an infinitely thin cylinder because walking on the outside curves away from the honey whereas walking on the inside curves towards the honey.

[retrosai]

Psychology student: That's a trap.

Commerce student: let's bring other ants in order to distribute risk and reward.

Le Science student...

[addct]

For anyone wondering this is the Fermet's principle... we also define reflection of light using this

[AbhisarRawat]

The ant opens a portal like Dr Strange and teleports to the honey

[DrBose]

What if Ant's doctor told Ant to take the longest road and walk most?

[AniketKumar-lwsu]

There is actually a very similar IOQM (Indian Olympiad Qualifier In Mathematics) PYQ 2019.
This was the toughest problem in the paper that year, now it's a standard problem which nearly everyone preparing for IOQM knows

[pravendrakumar]

Only tell me bro how TF I'm supposed to do this in my question paper

[vipinsingh]

One of the best ways to teach math I have found on YouTube. This is great. Keep them coming.

[wontpower]

You failed to mention that this method works because the transformation from the cylinder to the flat plan is isometric, meaning distances and angles are preserved

[vasudevjs]

I somehow found the answer in a few seconds😮.
I didnt think that this was right😅.
Its my first time actually answering the right answer in one of your videos.

[sohamadak]

Yeahh this is a famous method in straight line questions, alternatively this can be done by minimising the time by calculus

[russellesteban]

i play billiards, and this is a cool way to visualize cushion shots!

[Abhisruta]

@Host Can you solve a slightly modified version of the problem, if I give you a sphere, and one of it's latitude lines? Both the ant and piece of food are on the same hemisphere initially; And ant has to come back to its food touching the latitude traversing the shortest path, staying on the sphere.

[adityabanerjee]

How do these people describe such complex items in such easy way😮😮😮!!!

[nikhilgvd]

Couldn't it just roll over the surface horizontally without getting to the top vertically?

[bharathc]

Bro
Kindly explore mathematical equations which finds the shortest path too

Do add the equations after the visual representation