When do clock hands overlap? - Numberphile

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Videos by Brady Haran

[Wildlon]

This guy is my favourite maths commentator/ teacher in the entire world. He's just so enthusiastic and happy about maths and it's pretty endearing. There's not really anything he says that could be boring...

[oliverguidetti]

Dear Numberphile. I will watch and tip every video with Stoll. He is a gem who must be shined upon ❤️ if I were more gainfully employed I would offer more for more Stoll! His enthusiasm is fantastically emphatic.

[Electrolizr]

MARTY!! WE HAVE TO GO BACK! BACK TO THE FUTURE

[Jelle_NL]

Another way to solve it is to realize that the minutes pointer travels at 360 degrees per hour and the hour pointer travels at 30 degrees per hour. Their relative speed is 330 degrees meaning that they cross 330/360 times per hour - or more simply put - in intervals of 12/11 hours.

[garrettdennis]

Honestly he's one of my favorite people in numberphile, he so passionate about math

[antonfalu]

My first thought was "is it trivial that the eleven events are evenly spaced in time?". Sure enough, the clock doesn't care about rotation so every crossing can be thought of as the starting point.

[bretmanfan]

What a genius! I like how you're passionate this!

[super_]

Can you put a clock in a klein bottle?

[souverainer]

Here is another simple solution (Perhaps not as elegant):

The angular speed of the hour hand is v_h = 2*pi/(12*60*60) rads/sec
The angular speed of the minute hand is v_m = 2*pi/(60*60) rads/sec

So if they both start at 12:00, the minute hand will approach the hour hand at:
v_m - v_h = 11/12*2*pi/(60*60) rads/sec = v_a

So in 1 hour (2*pi rads), the two hands will meet at (think of a slower runner having a head start of 2*pi rads):

2*pi / v_a = 3927.273 seconds, which, modulo 2*pi rads is 327.273 secs, which is 1:05:27.2 (1:05 and 27.3 secs)

You can continue the same process for the next one, but this time start at 1:05:27

[rationalist]

Great one.... Helped me to get a quant problem

[WhovianMinecrafter]

this video legitimized the questions I asked as a little kid. the fact that a problem I thought of when bored is made into a video on numberphile is pretty cool

[Chris-P.-Bacon-III]

i love klein bottle guy
i dont care what the video is about if klein bottle guy is there
we need more klein bottle guy

[horizon]

I noticed if you round down to the minutes, there's a pattern of 5 minutes additional from an odd hour to an even hour, and 6 additional minutes from an even to an odd hour. This is a simple way to remember the times so if you happen to look at a digital clock (assuming it's in non 24 hour mode) and it's, say 4:21, you can be reminded that on an analogue clock the hands are crossing!

[hazhirfatih]

wtf, how many channels do you have, I just keep finding new ones.

[VirtualRiot]

I stopped the video after he explained the problem and got to the solution myself in 5 min, this is a really cool question though especially if you wanna keep a maths class busy.

[savaros]

I seriously asked myself this question so many times just out of sheer curiosity but never sat down and tried to figure it out. As soon as I did, it came almost instantly.

[joosmunneke]

Can't you turn this problem in some kind of Zeno's paradox? I mean, everytime the hour-hand approaches the minute-hand, the minute-hand has moved a little bit further. So the hour-hand has to approach the minute-hand again and so on..

[oliverguidetti]

This man must be protected at all costs.

[thomasr]

I watched the first 30 seconds of this video, went away and solved it then watched the video and you guys used my exact method!

[NassosConqueso]

I love his enthusiasm, he's always so energetic and happy!