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.
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.
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
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.
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!
@@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...
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.
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)
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?
"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. "
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 :>
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'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 -~-
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.
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.
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. =)
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 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.
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.
Thank you so much for your videos. You guys are...brilliant!
8 лет назад
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.
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.
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.
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.
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 :)
