Game of Cat and Mouse - Numberphile

Ben Sparks discusses the math behind a curious problem....
More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran

[PeridotFacet-FLCut-XG-ogxx]

You can't run, you can't hide, but you can swim in circle between two event horizons and make a dash to escape.

[victoria]

the mouse just needs to swim at the speed of light because if he does so the cat would go 4x the speed of light and you cant do that or the universe police will show up.

[im_a_sleepy_boy]

Wow Tom and Jerry is a lot more complex than I remember

[wallonice]

"That would be a tense moment for the mouse"
Yeah i'd also fear death if a gigantic chestnut-shell balloon hybrid came storming toward me

[cheshre_cat]

The mouse has a better character arc than most hollywood action heroes

[camilohiche]

Honestly this guy, as a Numberphile regular, is highly underrated. One of the best if not the best.

[panda]

9:36 - "the mouse can't dash from the center. So the obvious question is, where can it dash from?"
I was expecting the ad for dashlane to appear

[stixtheminer]

To answer brady's question, the mouse can escape with any ratio less than pi + 1.


the formula for the smaller circle is 1 - (pi/x) and the larger circle is just (1/x)
(1/x) = 1 - (pi/x)
(1 + pi)/x = 1
x = pi + 1

[WillRennar]

2:25 - Initial theory before watching any further:
-Starting from the center, the mouse has to cover distance _r_ going directly away from the cat.
-The cat has to cover half the circumference of the circle, or (2πr)/2, or πr.
-As the cat is going 4x as fast, and 4>π, the cat will get there before the mouse, and at that point the mouse will have a greater distance to go.

Conclusion: The mouse is doomed.
[resumes video]

12:25 - Took me exactly 10 minutes to realize I was wrong about the mouse being doomed.

[zarnox]

At first I thought the "press paws" meant my hands. No, it was a pun, and it took me nearly half the video to realise that.

[jerry]

I know this worst mouse ever is just a distraction to stop us using Parker Squares! You can’t fool me!

[BC]

Wow, mind blown. I kinda forgot about the circling which effectively decreases the distance to the shore. When the video started I immediately thought "When the cat is more than pi-times faster than the mouse the mouse will never make it.".
I love this channel and I say that as someone who failed at math.

[hotflashfoto]

As the mouse goes to that narrow sweet spot in an effort to increase the angle between himself and the cat, he could save a large measure of effort by heading toward the center until the angle was great enough, then swim toward the sweet spot again, arriving at just the right time to dash for the escape.


This was a fantastic presentation and I learned quite a bit from it. Thank you!

[johnchessant]

I loved the moment of realization when he hinted at how we can combine the two strategies to solve the problem.
He presented this problem and solution very well. This is truly what maths is all about!

P.S.: The number between 4.1 and 4.2 at 16:00 is in fact (pi + 1). It's a fun, easy exercise to work this out.

[leefisher]

Mouse uses circling tactic within sweet spot and gets 180 degrees from the cat.
Mouse dashes to the edge of the pond, with the cat close by, but not directly upon it.
Mouse shakes himself dry on the edge of the ... oops!

[AximVidya]

4m/s "That's a quick cat"
Has this guy ever seen an actual cat?

[vyzelliaveryllia]

When doing the circle method, what if the mouse sometimes run on a secant of the circle instead?
With this method, the cat should still run in the same direction as the circle method, but the mouse got a chance to reach another point of the circle a bit faster than the circle method (secant line is shorter than arc length).

[wallonice]

"Worst mouse ever"
Me: hold my pencil

[boriswilsoncreations]

0:15 - 0:40 how to design a t-shirt 😂😂😂 I think that was the fastest t-shirt design in the world lol

[maccollo]

The mouse can actually escape if the cat is less than approximately 4.6033 times faster than the mouse.
Hint: Once the mouse leaves the "safe zone" it doesn't have to dash radially.