The Seven Bridges of Königsberg - Numberphile
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- Опубліковано 21 вер 2024
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This video features Cliff Stoll... and the work of Leonhard Euler.
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I love this man. he's the only one who's sane.
You think he knows anything about dolphins?
which is ironic since he looks insane
HHGTTG reference?
Reminds me of Back to the Future's Doc.
Reminds me of Emo Philips
3:26 Ooh, ooh, OOFOOZELRUB oops.
Stay out of the water.
OMG I BARELY NOTICED
6:26 Let me see.. BULRFWAHA BAH BAH BAH BAH
Let me see how I'm doing this.
Dmitry Krasnapolsky ;;.
5:05 I can go around BLABLABLABLAVOOVOOVOOVOOVOOF and return to it.
OOFOOZELUb
You can never get enough of the Klein Bottle Guy
i certainly haven't
Intrepid G hahaaha
You are mistaken. :p
+Fester Blats You haven't. No one has. Trust me.
You think you have, but you don't
Cliff = Instant like.
yeaah boy
numberphile video = Instant like :]
Goat's got it.
Yeah!!
false.
i like how the subtitles include all the sound effects he made
*splashing water sounds*
Now i have to watch it again.
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"
@@FinBoyXD I'd love that, not that I need excuses., I've seen it about six times at least.
This man is passionate about what he's explaining !
If our teachers could be like him :)
:)
Martin Tessier :D
Every teacher I ever had was like that but then again it was the old school days.
I am a simple guy. I see this man in the thumbnail, I click on the video
Mashrur Ahmed Yafi when you see Klein bottles you are not a simple man anymore...
He's so enthusiastic and wholesome, he's the Bob Ross of mathematics
Cliff stoll is amazing
thought i was the only one!
me every time
A bag full of labeled smaller bags ! This guy can't be human :D
I have one or more of those... but not labelled.
I call them BOB...
Bag Of Bags.
@@RogerBarrauddo you also have a bag of all bags that don't contain themselves?
I wish he was my math teacher.
Today he was!
Were was he like 20 years
MATHS!!!
All great math teachers have this passion for mathematics and number theory.
Math Math Math Math Math Math Math Math Math Math Math Math
13:28 *hand casually grabs a klein bottle from the fourth dimension*
*TesseractYoink*!!!11!!
:-)
"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.
Relatable here....
Cliff Stoll is a national treasure.
*international treasure
How to solve any problem: just destroy two bridges :D
Thats how its done in USSR
Are you sure they were destroyed by ussr?
Except the problem of having no bridges at all.
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
"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 ;)
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.
I bet he is the best grandpa ever.
Only clicked for Mr. Klein...
Smoke Math Anyday
Ceazar Carr Mr. Klein is the best.
true true
Yep, I love how excited he is about math and just everything!
Mr. Klein was an actual person. en.m.wikipedia.org/wiki/Felix_Klein he was the mathematician who discovered/invented Klein bottle
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
Thank you - very kind
I would like to see a bridge made out of klein bottles
Closest thing would be the Möbius Strip bridge they're building in China.
i mean, aside from having a loopdeloop in the middle, it wouldnt be that hard.
but what would you walk on?
The inside of the bridge, of course!
But all bridges are already inside the bottle
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 solution is to make a bridge into a klien bottle so you can reuse the bridges upsidedown
Mom carey
True 🤔🎯.
12:20 Discrete Mathematics with Ducks
Yes, it's a great book by Sarah-Marie Belcastro. It wasn't a joke.
Yeah I agree. Very well-written book, nice demonstration, and ducks!
This dude is my favorite, he's so energetic and excited for math.
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.
How does Cliff not have his own TV show?
finfan7 yess we need that
It'd be like Bill Nye but for math
Unlike Bill he's an actual expert, too...
Roger Barraud Wait... so Bill Nye wasn't a science guy? 😉
Call it Klein Bottle Man
"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. "
he needs to be in more videos hes amazing
There will be some more
Yes!
Yes! I love adults that didn't grow. He's awesome
Yusss!!11!! :-)
@@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...
this guy took "The floor is lava" game to another level :D He is amazing
Normie
The floor is lava, level 2
It's the water phase
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!
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)
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)
Oh right yeah, the people in my 6form were a bit lazy and all took Decision over some of the harder modules :P
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
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?
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.
Thank you
Learnt already on Ted-Ed. Gonna watch it anyway, for Cliff Stoll...
ok
My impression of Cliff: Great Scott!!!
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.
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.
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!
passion is really overflowing from this man !
I love this guy. His passion is so over the top
I want the profressor's *po po po po* as my notification alert.
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
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 -~-
Maybe it only works for people who live on one island are willing to die on the second!? :)
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.
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
I'm sure you can get a boat ride, or go for a swim
A mission on Koenigsberg 1.
I subscribed this channel few hours ago, and suddenly it comes up with what I am working on right now.
by the way it said that it is a geometry of situation not location
But are the bridges measured in smoots nowadays?
There is only one such bridge.
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.
WarpRulez what a Parker Square smoots are.
That's just that one bridge in Boston/Cambridge
This comment made my day
Discreet Mathematics and ducks. I WANT THAT MATH BOOK.
Limited Edition
_Discrete Mathematics with Ducks_ is a real book, it wasn't a joke. It's by Sarah-Marie Belcastro.
Now I REALLY want that math book :D
Alius XD
Numberphile
What do you get if you add an ad to an ad?
Adception 😜
Klein bottle guy isn't the hero we deserve, but he is the hero we need.
Cliff Stoll is my favorite to have on your videos
Agreed 100%
...Now I have the urge to eat pizza again though... :-/
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.
*Me:* Hey it's the jumpy-pizza-bottle-guy!
_Clicks on the video so fast...!_
tfw you're watching Numberphile and he suddenly whips out his Klein bottle.
I love this guy. He treats math with such enthusiasm and excitement, as a mathematician myself it really get's me motivated!
this man is incredible, endearing, humble, and insane - makes me not want to be a stoic engineer, and to be outwardly compassionate. thank you.
I found a way to beat the problem by swimming.
I found a dry solution: a river always has a start, so you can loop around the source.
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.
You may have to hike through all of easter Europe for that though...
I have a truly marvellous solution, but the boundaries of this comment are too small to contain it.
This man is 200% enthusiasm and he restores life and happiness to my husk of a soul.
I'm curious. Is this Cliff Stoll the same Cliff Stoll who wrote Cuckoo's Egg?
yes, that's him
wow.
well, I just downloaded a sample... that looks interesting.
thanks for the info
This explains much of why I enjoyed the book so much. ;-] Thanks
Thanks for the tip, I enjoy Cliffs vids on Numberphile so much I ordered a copy as soon as I read the synopsis
Woah. Read the books years ago...and then I find him on UA-cam on one of my favorite channels. Awesome.
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. =)
Cliff is my caffeine.
+superj1e2z6 more like cocaine, at the rate he goes... :-/
By far my favorite numberphile host/speaker guy
"What's now Russia or Poland, hard to say which."
As a Pole, I approve.
I'm so happy to see another Cliff Stoll video.
his enthusiasm is infectious
I love this guy so much. Thank you for making videos with him
Just watched his TED talk "The call to learn".
What a great and unique man :)
just watched that talk, what an entertaining guy he his. thanks for that :)
I can listen to him talking all day
A video about the famous problem with the 7 seven bridges of Königsberg with Cliff...insta favorite
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.
DaBoff99 Not rly :P
I need a book on Discrete Mathematics With Ducks
Go to DuckDuckGo (or Google if you're lazy) and search for Discrete Mathematics With Ducks. You're welcome.
This gentleman is probably almost twice my age but he has twice the energy I do. Kudos to you sir.
This has got to be the nicest man I've come across on the internet.
He thinks nothing of recreating a math puzzle on his office floor with sheets and wooden boards. I love this guy.
That camera angle :D i imagine you stood on the table or stool
I wanted the "Google Maps" view!
neat :)
Cliff thank you for spiking my interest for math and physics again and again
"Discrete mathematics with ducks." --Cliff Stoll
anyone else think this old man is adorable? he's like a kid that never grew up.... love it...
There actually are 7 bridges again in Kaliningrad, only difference is that 5 bridges are on the other island than before.
or 8 if we count also one bridge just for pedestrians - Russia already solved the problem by having even number of bridges.
Adalbertus Malleus As long as you start on one island and stop on the other you can cross all 8 bridges.
Having a hard day. Cliff cheers me up. Thanks Cliff.
Ah I love Cliff videos, he's always so excited which makes me happy and learn better!
All the love
And that's why I love numberphile and math, knowledge with huge enthusiasm ❤️
I LOVE THIS MAN! MOREEEEE . He deserves to have a complete channel to himself.
As soon as I saw Cliff Stoll in the thumbnail, I clicked. It was nearly reflexive.
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
It took me 11 minutes to realize you didn’t have to get home, but I still learned a lot and thought of ways to solve it. That’s the beauty of math
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.
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.
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.
Swag Monee It depends on how fast you walk ;-)
Víktor Bautista i Roca
lol true, but then it wouldn't be a stroll, it would be a nice Sunday sprint
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.
Cliff is so excited explaining math... I love his videos. Thank you.
Thank you so much for your videos. You guys are...brilliant!
What an amazing story, I bet my Computer Graphics teacher will like to hear it since we started talking about topology last week.
His sheer enthusiasm makes me excited about whatever he's talking about.
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.
Rest in peace Königsberg... You were once a beautiful city
Oh and Euler must've been a really bright individual! I would have loved to have a conversation with him, which unfortunately will never happen!
I love this man.
Same here, he is fantastic just like this channel. Finally a way to have fun in maths😂😂
I wish I had enough Klein bottles to pick one up and make a point with it at any moment
Can you do a video on Cliff's DeLorean?
Great scott!
This was great. I learned about this problem when I was getting my Computer Science degree in the 70s. I haven't thought about it since. At the time, Euler was just a name. It is cool to see the history of this problem brought to life.
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.
Honestly, you could have Cliff talk about anything and I'd find it interesting. He's just such a wonderful speaker.
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 a simple man, I see Mr. Klein Bottle in the thumbnail, I watch, I like
Looks like Doc Emmet Brown found a new job in our timeline.
I love this guy, videos that feature him are always amazing. The legit enthusiasm really makes the video.
I still wonder what this guy uses.
or Meth
Why not both?
this professor brings me unimaginable joy
can you imagine how much fun homework would have been if this guy was your dad when you were a kid?
Wow, now I can solve one of those "trace a path over this object without crossing any line twice" problems! Thanks Cliff! and Leonhard Euler of course.
I love this guy, he sounds a little like INCONCEIVABLE!
I love how Cliff Stoll helped solve and International manhunt for a hacker, and everyone here just knows him as the Klien Bottle Guy.