The Seven Bridges of Königsberg - Numberphile
Ғылым және технология
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This video features Cliff Stoll... and the work of Leonhard Euler.
More Cliff videos: bit.ly/Cliff_Videos
Cliff's Klein Bottles: bit.ly/ACME_Klein
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Пікірлер: 1 437
I love this man. he's the only one who's sane.
@justanotherbaldbastard2193
7 жыл бұрын
You think he knows anything about dolphins?
@noredine
7 жыл бұрын
which is ironic since he looks insane
@zoranhacker
7 жыл бұрын
HHGTTG reference?
@senorsushi6625
7 жыл бұрын
Reminds me of Back to the Future's Doc.
@tazjam12
7 жыл бұрын
Reminds me of Emo Philips
You can never get enough of the Klein Bottle Guy
@mrdontgiveafuck3
7 жыл бұрын
i certainly haven't
@tiagotralhao-smith3883
7 жыл бұрын
Intrepid G hahaaha
@Clint945
7 жыл бұрын
You are mistaken. :p
@matteoverni4183
7 жыл бұрын
+Fester Blats You haven't. No one has. Trust me.
@Vodboi
7 жыл бұрын
You think you have, but you don't
3:26 Ooh, ooh, OOFOOZELRUB oops. Stay out of the water.
@armoredriot2716
5 жыл бұрын
OMG I BARELY NOTICED
@dmitrykrasnapolsky1798
5 жыл бұрын
6:26 Let me see.. BULRFWAHA BAH BAH BAH BAH Let me see how I'm doing this.
@woraphatlaowrattana4290
4 жыл бұрын
Dmitry Krasnapolsky ;;.
@Jivvi
4 жыл бұрын
5:05 I can go around BLABLABLABLAVOOVOOVOOVOOVOOF and return to it.
@casvel4942
3 жыл бұрын
OOFOOZELUb
Cliff = Instant like.
@StixerX
7 жыл бұрын
yeaah boy
@AuroCords
7 жыл бұрын
numberphile video = Instant like :]
@RogerBarraud
6 жыл бұрын
Goat's got it.
@aaryunik
3 жыл бұрын
Yeah!!
@Triantalex
8 ай бұрын
false.
I wish he was my math teacher.
@numberphile
7 жыл бұрын
Today he was!
@oneofspades
7 жыл бұрын
Were was he like 20 years
@the7th494
7 жыл бұрын
MATHS!!!
@TaleOfNobody
7 жыл бұрын
All great math teachers have this passion for mathematics and number theory.
@philo-
7 жыл бұрын
Math Math Math Math Math Math Math Math Math Math Math Math
i like how the subtitles include all the sound effects he made
@sebastianzaczek
6 жыл бұрын
*splashing water sounds*
@FinBoyXD
5 жыл бұрын
Now i have to watch it again.
@gabrielbraun5428
5 жыл бұрын
Clif: "Try here, go there, d-d-d-d-d-d", CC: "Try here, go there. [sound of a series of choices]" And of course, CC: "There's [sic] two islands"
@omikronweapon
4 жыл бұрын
@@FinBoyXD I'd love that, not that I need excuses., I've seen it about six times at least.
I am a simple guy. I see this man in the thumbnail, I click on the video
@davidwilliams9534
6 жыл бұрын
Mashrur Ahmed Yafi when you see Klein bottles you are not a simple man anymore...
@Ueichen
5 жыл бұрын
He's so enthusiastic and wholesome, he's the Bob Ross of mathematics
@nodawg
5 жыл бұрын
Cliff stoll is amazing
@squidy9078
5 жыл бұрын
thought i was the only one!
@Paul-yu4ep
5 жыл бұрын
me every time
A bag full of labeled smaller bags ! This guy can't be human :D
@RogerBarraud
6 жыл бұрын
I have one or more of those... but not labelled. I call them BOB... Bag Of Bags.
@thedoublek4816
23 күн бұрын
@@RogerBarrauddo you also have a bag of all bags that don't contain themselves?
This man is passionate about what he's explaining ! If our teachers could be like him :)
@numberphile
7 жыл бұрын
:)
@katilinom7691
7 жыл бұрын
Martin Tessier :D
@dannygjk
2 жыл бұрын
Every teacher I ever had was like that but then again it was the old school days.
Only clicked for Mr. Klein...
@kmyc89
7 жыл бұрын
Smoke Math Anyday
@MrCreeper1O2
7 жыл бұрын
Ceazar Carr Mr. Klein is the best.
@gordogregory501
7 жыл бұрын
true true
@dahveed284
7 жыл бұрын
Yep, I love how excited he is about math and just everything!
@aeroscience9834
7 жыл бұрын
Mr. Klein was an actual person. en.m.wikipedia.org/wiki/Felix_Klein he was the mathematician who discovered/invented Klein bottle
13:28 *hand casually grabs a klein bottle from the fourth dimension*
@RogerBarraud
6 жыл бұрын
*TesseractYoink*!!!11!! :-)
the solution is to make a bridge into a klien bottle so you can reuse the bridges upsidedown
@stevenpeterson3734
4 жыл бұрын
Mom carey
@PC_Simo
Жыл бұрын
True 🤔🎯.
I would like to see a bridge made out of klein bottles
@christianmitchell499
7 жыл бұрын
Closest thing would be the Möbius Strip bridge they're building in China.
@WeAreGRID
7 жыл бұрын
i mean, aside from having a loopdeloop in the middle, it wouldnt be that hard.
@pizzahorder7721
7 жыл бұрын
but what would you walk on?
@MrSonny6155
6 жыл бұрын
The inside of the bridge, of course!
@yashgaikwad7516
6 жыл бұрын
But all bridges are already inside the bottle
Cliff Stoll is a national treasure.
@thewolfofthestars1847
7 жыл бұрын
*international treasure
I bet he is the best grandpa ever.
"this may give you an answer, but it doesn't give you an understanding" this is exactly what schools are doing right now, and it needs to change.
@s-nonymous0273
3 жыл бұрын
Relatable here....
How to solve any problem: just destroy two bridges :D Thats how its done in USSR
@Fabelaz
7 жыл бұрын
Are you sure they were destroyed by ussr?
@kauhanen44
7 жыл бұрын
Except the problem of having no bridges at all.
@newparsec
7 жыл бұрын
Im not sure, but: 1. There was war 2. USSR was there This tale is equal the tales about "russians are bears on monocycles, drinking vodka and playing balalaika". Nobody in Russia saw bear on monocycle on streets, no bear drinking vodka and no bear can play balalaika. But tale exists :D
@newparsec
7 жыл бұрын
"having no bridge" is antipode to "having bridge", so "destroy bridge" is antipode to "destroy no bridge". So Destroying no bridge is the solution of the problem of having no bridges. If you have no bridge, destroy no bridge and you will not have no bridge ;)
@Fabelaz
7 жыл бұрын
Канал "Парсек". EVE Online. Гайды для новичков Well, first of all, one can just google that information to be exact. Who controlled the territory then and who bombed it. Knowing exact time period can give us a lot in this discussion. And your knowledge of math logics doesn't look quite well for me. Though I myself didn't study if tor quite some time now, so I might also be wrong here.
This video made my day, some interesting maths and one of my favorite guests, Cliff. The keeping him honest about staying on the bridges made me laugh. Keep up the good work guys
@numberphile
7 жыл бұрын
Thank you - very kind
How does Cliff not have his own TV show?
@ararepepe974
6 жыл бұрын
finfan7 yess we need that
@milesbrown2261
6 жыл бұрын
It'd be like Bill Nye but for math
@RogerBarraud
6 жыл бұрын
Unlike Bill he's an actual expert, too...
@andreastrange3429
6 жыл бұрын
Roger Barraud Wait... so Bill Nye wasn't a science guy? 😉
@tulip6963
5 жыл бұрын
Call it Klein Bottle Man
12:20 Discrete Mathematics with Ducks
@error.418
7 жыл бұрын
Yes, it's a great book by Sarah-Marie Belcastro. It wasn't a joke.
@warmpianist
7 жыл бұрын
Yeah I agree. Very well-written book, nice demonstration, and ducks!
I've seen this problem before, but I love listening and watching Cliff get excited about mathematics and whatnot. He's the kind of old guy I wanna be when I'm old.
The floor is lava, level 2
@TheJFARod
4 жыл бұрын
It's the water phase
This dude is my favorite, he's so energetic and excited for math.
this guy took "The floor is lava" game to another level :D He is amazing
@Cjnw
5 жыл бұрын
Normie
he needs to be in more videos hes amazing
@numberphile
7 жыл бұрын
There will be some more
@stinkytoby
7 жыл бұрын
Yes!
@afbdreds
7 жыл бұрын
Yes! I love adults that didn't grow. He's awesome
@RogerBarraud
6 жыл бұрын
Yusss!!11!! :-)
@SumriseHD
3 жыл бұрын
@@afbdreds It has nothing to do with growing up. People often mistake growing up with getting pensive. Sadly, for many people adulthood brings along this in my opinion bad mood, but some become adults without becoming depressed or sad and those are the people often described as adult childs even though they're not...
They actually teach this in A Level maths now as compulsory knowledge lol, read it it in the D1 book. (I love this guy's teaching persona, maths would have been so much more fun with him as a teacher)
@SithBowman
7 жыл бұрын
D1 isn't always a compulsory module for A Level Maths, it was used as a module for Further Maths with my exam board (MEI)
@llF4TEll
7 жыл бұрын
Oh right yeah, the people in my 6form were a bit lazy and all took Decision over some of the harder modules :P
@SithBowman
7 жыл бұрын
CDDGR My 6th form chose to do M1 + S1 alongside C1-4, I would hazard a guess that out of Mechanics and Statistics that students would prefer S1 over M1, S1 is easy enough for smarter Yr11s to do
@llF4TEll
7 жыл бұрын
Yeah it was Mechanics that most people opted out of, which was ridiculous to me because many were doing Physics anyway XD But yes isn't S1 pretty much just GCSE stats?
@SithBowman
7 жыл бұрын
CDDGR S1 had more topics with calculations in them, GCSE stats seemed to involve more statistics reasoning
I just love this guy, always inspires me to enjoy every single problem.
@numberphile
7 жыл бұрын
Thank you
13:22 -- 13:48 I love this part of the video…especially the last few seconds when you see how truly excited this makes him feel and how passionate he is about this topic.
Learnt already on Ted-Ed. Gonna watch it anyway, for Cliff Stoll...
@ooknkoo1
7 жыл бұрын
ok
@harrytsang1501
7 жыл бұрын
My impression of Cliff: Great Scott!!!
@KnakuanaRka
5 жыл бұрын
Harry Tsang Maybe I don’t remember Doc Brown all that well because it’s been a while since I saw BttF, but I kept hearing Goofy.
I want the profressor's *po po po po* as my notification alert.
@homemadelemonade976
7 жыл бұрын
Jake Roosenbloom you can do it, just dl the video mp3, find the part and cut it out, format it and use it as a ringtone
@AinaweeUAE
7 жыл бұрын
GREAT IDEA! I am gonna do that now!
There's only one problem for today's konigsberg with 5 bridges. When one is visiting it how does he get onto one island without using one of the bridges -~-
@numberphile
7 жыл бұрын
Maybe it only works for people who live on one island are willing to die on the second!? :)
@everdale8920
7 жыл бұрын
If the problem is defined as "Can I do a Sunday walk across all 5 bridges and end up where I started?" then let's say you take your car to an island at Saturday and check in at a hotel. On Sunday, you start on an island.
@peterw9006
7 жыл бұрын
everdale but there´s the thing. you dont end up on the same island but on the other and yout dont get to ur car nor hotel
@GeeItSomeLaldy
7 жыл бұрын
I'm sure you can get a boat ride, or go for a swim
@2Cerealbox
7 жыл бұрын
A mission on Koenigsberg 1.
But are the bridges measured in smoots nowadays?
@WarpRulez
7 жыл бұрын
There is only one such bridge.
@2Cerealbox
7 жыл бұрын
There are no smoots in topology. Two things are topologically equivalent if there is a continuous mapping from one onto the other. Smoots don't work with rubber-band geometry.
@sleepingsaucer3801
7 жыл бұрын
WarpRulez what a Parker Square smoots are.
@lucashoffses9019
7 жыл бұрын
That's just that one bridge in Boston/Cambridge
@nichrun
7 жыл бұрын
This comment made my day
"Euler's solution for this created graph theory. Euler's solution to this created topology. All of this from a guy who 'Oh yeah, I've got a little of time to think about a problem that I heard about from people going on sunday mornings.' Thats brilliance. "
passion is really overflowing from this man !
I love this guy. His passion is so over the top
Pens and paper can only convey so much. It's beautiful to learn by watching a maths lunatic with a burning passion, a few 2×4's and some bedsheets constructing and showing us the challenge.
Cliff Stoll is my favorite to have on your videos
@Charliemmag
7 жыл бұрын
Agreed 100%
@RogerBarraud
6 жыл бұрын
...Now I have the urge to eat pizza again though... :-/
I think if I had this guy as my math teacher, it wouldn't have taken me 20 years to be interested in math. Very glad that it turned out that I like programming, they ended up being closely related :>
This guy's passion for math and silliness is so infectious. If Dr. Stoll has any other fun old problems to play out I'd love to see it!
I'm curious. Is this Cliff Stoll the same Cliff Stoll who wrote Cuckoo's Egg?
@red_isopat
7 жыл бұрын
yes, that's him
@thoperSought
7 жыл бұрын
wow. well, I just downloaded a sample... that looks interesting. thanks for the info
@llearch
7 жыл бұрын
This explains much of why I enjoyed the book so much. ;-] Thanks
@brickscratch
7 жыл бұрын
Thanks for the tip, I enjoy Cliffs vids on Numberphile so much I ordered a copy as soon as I read the synopsis
@Lizardboythelazy
7 жыл бұрын
Woah. Read the books years ago...and then I find him on KZread on one of my favorite channels. Awesome.
Discreet Mathematics and ducks. I WANT THAT MATH BOOK.
@numberphile
7 жыл бұрын
Limited Edition
@error.418
7 жыл бұрын
_Discrete Mathematics with Ducks_ is a real book, it wasn't a joke. It's by Sarah-Marie Belcastro.
@F2PAlius
7 жыл бұрын
Now I REALLY want that math book :D
@michagrill9432
7 жыл бұрын
Alius XD
@michagrill9432
7 жыл бұрын
Numberphile What do you get if you add an ad to an ad? Adception 😜
tfw you're watching Numberphile and he suddenly whips out his Klein bottle.
Klein bottle guy isn't the hero we deserve, but he is the hero we need.
his enthusiasm is infectious
Cliff is my caffeine.
@RogerBarraud
6 жыл бұрын
+superj1e2z6 more like cocaine, at the rate he goes... :-/
I subscribed this channel few hours ago, and suddenly it comes up with what I am working on right now.
@riyanputra223
7 жыл бұрын
by the way it said that it is a geometry of situation not location
I'm a math teacher, and I've taught the 7 Bridges of Konigsberg to grades from 2nd up through 12th and every single time it's been a winner of a lesson! It never fails to excite and kid, they come running up to the board to try to figure out how to do either an Eulerian Path or an Eulerian Circuit on the map of Koningsberg. And then before you know it I'd have elementary school kids talking graph theory! I've always thought that all 7 bridges fell in WWII and that 5 happened to be rebuilt. Now providing you have a helicopter you can do an Eulerian Path! Cliff is an inspiration. I'd love to be the kind of teacher that he is. It's what I strive for everyday! I'm a proud customer of Acme Klein Bottle, and this year a student 3D-Printed me a really cool glittery orange one!
I found a way to beat the problem by swimming.
@recklessroges
7 жыл бұрын
I found a dry solution: a river always has a start, so you can loop around the source.
@jmiquelmb
7 жыл бұрын
I found another solution: B and C are the same if you circumnavigate the world and reach the other side without crossing any of the 7 bridges.
@baronDioxid
7 жыл бұрын
You may have to hike through all of easter Europe for that though...
@fergusmaclachlan1404
7 жыл бұрын
I have a truly marvellous solution, but the boundaries of this comment are too small to contain it.
*Me:* Hey it's the jumpy-pizza-bottle-guy! _Clicks on the video so fast...!_
That camera angle :D i imagine you stood on the table or stool
@numberphile
7 жыл бұрын
I wanted the "Google Maps" view!
@niabride7636
7 жыл бұрын
neat :)
I love this guy so much. Thank you for making videos with him
@maldoran9150
7 жыл бұрын
Just watched his TED talk "The call to learn". What a great and unique man :)
@Panj0
7 жыл бұрын
just watched that talk, what an entertaining guy he his. thanks for that :)
I love the randomness of "I'll walk over my third bridge backwards." And all the other wonderful diversions Cliff throws into his videos. All the while being contagiously enthusiastic, yet accurate and communicative. I was pretty familiar with this problem, so almost skipped this video. Obviously I know better now, and will hunt down all his others. It's not the destination that's important sometimes; it's the journey.
There actually are 7 bridges again in Kaliningrad, only difference is that 5 bridges are on the other island than before.
@JohnHammer21
7 жыл бұрын
or 8 if we count also one bridge just for pedestrians - Russia already solved the problem by having even number of bridges.
@ragnkja
7 жыл бұрын
Adalbertus Malleus As long as you start on one island and stop on the other you can cross all 8 bridges.
By far my favorite numberphile host/speaker guy
I love this guy. He treats math with such enthusiasm and excitement, as a mathematician myself it really get's me motivated!
Can you do a video on Cliff's DeLorean?
@toweypat
5 жыл бұрын
Great scott!
Ah I love Cliff videos, he's always so excited which makes me happy and learn better! All the love
I can listen to him talking all day
I love this guy, videos that feature him are always amazing. The legit enthusiasm really makes the video.
Cliff is so excited explaining math... I love his videos. Thank you.
A video about the famous problem with the 7 seven bridges of Königsberg with Cliff...insta favorite
@DaBoff99
7 жыл бұрын
Same. Have you listened to A Brief History of Mathematics BBC Radio 4 by Marcus du Sautoy, this problem is mentioned in the episoe on Euler.
@marshmelows
7 жыл бұрын
DaBoff99 Not rly :P
I love this man.
@schoey6956
7 жыл бұрын
Same here, he is fantastic just like this channel. Finally a way to have fun in maths😂😂
Thank you so much for your videos. You guys are...brilliant!
I LOVE THIS MAN! MOREEEEE . He deserves to have a complete channel to himself.
This man is 200% enthusiasm and he restores life and happiness to my husk of a soul.
It's just awesome to see how Cliff loves what he is doing. Im so entertained by him and im learining something. Thats really rare. Thank you and i hope to see much more Videos from him :)
I'm so happy to see another Cliff Stoll video.
Having a hard day. Cliff cheers me up. Thanks Cliff.
9:26 I think it's worth noting that there can only ever be an even number of islands with an odd number of bridges attached to them. So you will never have exactly one or three islands with an odd number of bridges attached to them. This is because each bridge increases the amount of attached bridges on exactly two islands. Therefore the sum of the amount of bridges attached to all the islands must be even. Therefore there must be an even number of islands with an odd number of bridges attached to them.
I wish I had enough Klein bottles to pick one up and make a point with it at any moment
Cliff thank you for spiking my interest for math and physics again and again
I completely love the way it has been presented.
Looks like Doc Emmet Brown found a new job in our timeline.
This guy has got to be my favourite!
Cliff makes every video so entertaining and enjoyable
You're revamping my childhood classroom experience. I love it. Beautiful story. Thanks for the nostalgia!
I need a book on Discrete Mathematics With Ducks
@daanwilmer
7 жыл бұрын
Go to DuckDuckGo (or Google if you're lazy) and search for Discrete Mathematics With Ducks. You're welcome.
As for the current situation, a combination of Wiki and Google Maps informs us that two of the original bridges were bombed in WWII, two were later demolished and replaced by a modern road (no stopping for cars, but there are footpaths running alongside plus steps to enable pedestrians to explore the island - Google labels this as "Leninskiy pr."), one was later rebuilt, and two new bridges have been opened (one joint road/rail - "Zheleznodorozhnaya ul.", one pedestrian only) - so there are bridges in five of the original seven locations, but only two are original. There's also a road crossing one island which doesn't have any exits / entrances on it nor a footpath ("ul. 2-y estakadnyy most"), so that can likely be ignored. So now for a pedestrian: B-C has one bridge, B-A has one bridge, A-C has one bridge, C-D has two bridges, D-A has one bridge and D-B has one bridge - so B has three bridges, A has three bridges, C has four bridges and D has four bridges. For a motorist: B-C has three bridges (two pass over the islands but have nowhere to stop or pull off), C-D has one bridge, D-A has one bridge and D-B has one bridge - so B has four bridges, A has one bridge, C has four bridges and D has three bridges.
And that's why I love numberphile and math, knowledge with huge enthusiasm ❤️
The beauty of science and scientists never ceases to take my breath away.
This has got to be the nicest man I've come across on the internet.
There's a small trick. In fact, C and B are the same land mass. You start in A, go to B and back, to C and back, cross to island D, go to B, make a long walk to wherever the river is born, come back on C side of the river, and cross to island D.
@swagmonee5699
7 жыл бұрын
Víktor Bautista i Roca But to make it all the way around from C to B wouldn't make a Sunday stroll. That would take a whole day's trip.
@swagmonee5699
7 жыл бұрын
Víktor Bautista i Roca But to make it all the way around from C to B wouldn't make a Sunday stroll. That would take a whole day's trip.
7 жыл бұрын
Swag Monee It depends on how fast you walk ;-)
@swagmonee5699
7 жыл бұрын
Víktor Bautista i Roca lol true, but then it wouldn't be a stroll, it would be a nice Sunday sprint
@croutonicus
7 жыл бұрын
If C and B are the same land mass they have a combined even number of bridges (6) and there are two other islands (A and D) with odd numbers, so the theorem still holds as long as you start in A or D.
I adore this guy, he's amazing at making education fun and has a funny "crazy with passion for his field"-thing going on. I'd love to have him as my university professor.
I love how much you loved making that video! :D
"Discrete mathematics with ducks." --Cliff Stoll
"What's now Russia or Poland, hard to say which." As a Pole, I approve.
Mr. Steeples (my 7th grade math teacher) introduced me to this problem over 20 years ago. This problem is the reason I grew up to be a math teacher myself. It totally changed my perception of math. =)
you have brought me another video involving this man, I have been appeased.
I love Cliff, I wish we could have a chat in person or something, he's really interesting and gives really good points... Actually now that I think of it I really wish he was my maths teacher
I still wonder what this guy uses.
@OwenPrescott
7 жыл бұрын
or Meth
@WhiteThunder121
7 жыл бұрын
Why not both?
this professor brings me unimaginable joy
I'm always excited to see more stuff about topology on numberphile.
can you imagine how much fun homework would have been if this guy was your dad when you were a kid?
What an amazing story, I bet my Computer Graphics teacher will like to hear it since we started talking about topology last week.
this man is incredible, endearing, humble, and insane - makes me not want to be a stoic engineer, and to be outwardly compassionate. thank you.
This man is absolutely fantastic.
A wild kleinbottle appears at the end
I love this guy, he sounds a little like INCONCEIVABLE!
Great Video! I love Cliff Stoll's personality.
Thank you, Dr. Stoll. That was great!