Brady needs more appreciation for how good he is at asking presenters the right questions to help illuminate the topic for the viewer.

@numberphile

4 жыл бұрын

If you are subscribed (and have alerts on) then that is all the appreciation I need! :)

@vtron9832

4 жыл бұрын

Numberphile I did both, you deserve it!

@nikanj

4 жыл бұрын

Absolutely. I mean I'm pretty sure he already knows what graphs are. They talk about them on computerphile all the time. He's asking purely on behalf of the audience.

@Roxfox

4 жыл бұрын

@@nikanj That's what makes it impressive. It's so hard to imagine not knowing what you know so that you can make sure other people learn it.

@ragnkja

4 жыл бұрын

Myrmidon Not to mention that James Grime already mentioned planar graphs in the four-colour theorem video.

The embedding part is quite useful in circuit design and circuit analysis. A cross-over in an electrical circuit can mean a short-circuit. You can work around it by inserting pass-throughs or even little wires that act like bridges. But the best way is to just be smart with your wiring and ensure it never crosses over itself if it can be helped. Basically, math like this can help you save money in circuits.

4 жыл бұрын

Or for example if you can design a tram system in a way that the tram lines connect the stations as a planar graph, then you can be sure that no tram ever needs to wait for another. That makes planning their times much easier.

@cicci0salsicci0

4 жыл бұрын

Also in E/R modeling in database design.

4 жыл бұрын

Molecules are also much nicer to draw if they can be arranged as a planar graph. I actually don't know how it would be done otherwise. Usually Chemists then become lazy and just write "C60".

@EmilienGosselin

4 жыл бұрын

Yup I've been there

@EdwardCoffey

4 жыл бұрын

@ though in the specific case of C60, it can be represented as a planar graph (its Schlegel diagram).

When I studied computer science I visited a course about bioinformatics and the prof kept talking about graphs like this... and after a while you noticed half the audience giving blank stares... he was really confused until I asked some of them if maybe they were thinking about the x-y kind. Turns out someone sent some biologists to the lecture and contrary to computer scientists they had never heard about THIS kind of graph -_-

In Dutch we actually have 2 different words: 'grafiek' is a graph with a function plotted on it, 'graaf' is a graph with vertices & edges.

@ruinenlust_

4 жыл бұрын

If you'd tell me, a Dutch person, that you'd like me to draw a 'graph'.... I'd draw a tombstone. We don't have the word 'graph' in our language.

@PeterVC

4 жыл бұрын

@@ruinenlust_ Damn auto-correct... I had written 'grafe' which was actually also incorrect, it's "graaf" (but not as in "count"), not "grafe". Sorry about that.

@ruinenlust_

4 жыл бұрын

@@PeterVC :)

@PeterVC

4 жыл бұрын

@@busimagen If you mean a "glyph" (sometime indeed also called "graph"), we call that "glief". While a "grapheme" is a "grafeem". So it's quite close to each other.

@ruinenlust_

4 жыл бұрын

@@busimagen Not really, we use the term 'staafdiagram' for bar graph. Dutch is like german in their usage of pasting words together. So you should be able to guess what a 'cirkeldiagram' is :) I don't fully understand your second example of graph?

Correction at 13:58 - remove the word "not". Continues with "Perfect Graphs" at kzread.info/dash/bejne/dWiO1Jacf7nTaco.html

@sigggo

4 жыл бұрын

Numberphile kul

@Muhammad-kc4yl

4 жыл бұрын

Thank You, For The Video

@radio4active

4 жыл бұрын

Simon Tatham's Puzzle Collection has a game called "untangle" that essentially tasks you with making a graph planar

@christinewen8310

4 жыл бұрын

So sexy!

@S1940ful

4 жыл бұрын

Cool video! BTW, is that Omega Speedmaster Moonwatch on your wrist?

I am actually surprised, that over so long time of the show running, we have not encountered graph topics. Isn't it interesting? This is a whole new dimension of videos coming on this topic :)

Title: Planar Graphs Thumbnail: *is not a planar graph*

@souleater9189

4 жыл бұрын

but it is one of the two key subgraphs that help distinguish planar vs non-planar

@cizdramasnedalm8055

4 жыл бұрын

Strictly speaking, a thumbnail is a digital image consisting of some number of pixels organized in a N x M grid. Depending on what you think the most natural way to connect the vertices is (for example, connecting each pixel to the next pixel in its row and connecting the last pixel in a row to the first pixel in the next row, or simply connecting the pixels in a lattice), I'd argue that any thumbnail is in fact a planar graph. Of course, you can go on to say that a digital image is nothing but a sequence of bits, or that a sequence of bits is nothing more than a series of voltage measurements, or that a series of voltage measurements is just a bunch of particles moving around in particular ways we've ascribed meaning to. In that case I think we've got bigger concerns than whether a graph is planar, but it certainly would provide an interesting discussion.

@oliverhoare6779

4 жыл бұрын

@@cizdramasnedalm8055 Ok, Neil deGrasse. Technically what I'm saying here are just pixels in a grid, so do interpret the following pixels- "pedantic asshole"- however you want.

@cizdramasnedalm8055

4 жыл бұрын

@@oliverhoare6779 Hey friend, there's no need to get all upset over a simple comment. I was just being pedantic for the sake of humor. Admittedly, the humor might have not been all that amazing, but still I don't feel like I deserved that.

@oliverhoare6779

4 жыл бұрын

@@cizdramasnedalm8055 Fair enough, my bad

Heh, I remember very well when four colors theorem was a mere conjecture, and pretty notorious one.

@Zeus.2459

4 жыл бұрын

ok boomer

@bazoo513

4 жыл бұрын

@@Zeus.2459 :o)

High schoolers and younger students are forced to go through the whole calculus series before even being introduced to this kind of finite maths (which is relied upon heavily in computer science and other data-driven fields) and the sprawling field of mathematics, and as a result a disheartening number of students get overwhelmed and overtaken by the workload and the maddening lack of an answer to the question of "when will we use this?". With maths like this it's possible to visualize and explain real-life applications fairly easily, and I don't think you'd necessarily need to have mastered calculus to understand the basic concepts. Maybe someday we can restructure the mathematics curriculum to include elementary non-calculus courses so that students don't have to wait until they are university sophomores to at least be introduced to these important problems.

@robertunderwood1011

4 жыл бұрын

Agree thoroughly. So much exciting stuff and fairly easy to explain that never gets introduced to high school students. KNOTHEORY, fun.

@plokki456

4 жыл бұрын

From my personal experience, I enjoyed several years of calculus way more than a few hours of graph theory. But I guess it's a matter of taste. Even though graph theory can be useful, I didn't find it as ground breaking/mind blowing as what we learnt in other fields of math.

@rmsgrey

4 жыл бұрын

There are a couple of reasons why graph theory doesn't get a lot of time in schools: One is that it's still a relatively recent area of mathematics, and it takes time for things to filter down to school-level - first you need enough academics to take an interest for it to start producing useful/interesting results, then you need there to be an interest in having graduates already know something about the area, and for there to be lecturers willing to teach it. That then starts getting you maths graduates who have some awareness of it. Once you have enough maths graduates familiar with graph theory (or whatever), then they can start slipping it into school syllabuses, and there should be staff available to teach it. Another is that there's not a lot of material that depends on understanding graph theory in order to learn it. In order to follow a course on complex analysis, you need to be familiar with complex numbers and with analysis, which in turn requires proficiency with algebra, and basic arithmetic, so there's a tendency to cover the material that's needed in order to progress to advanced courses rather than material that could be studied much earlier, but isn't a prerequisite for any other courses.

@dr_arcula

4 жыл бұрын

While I partially agree with you, I think you need to understand that all these interesting and thought provoking bits of information is just that. Bits. On top of an arguably huge mountains of boring math. Which is what made them so special in the first place. Importance of calculus is so underrated. And I don't even use calculus. My job is far removed from math. And yet wherever I look, I can see it's distinct impression. Ever wondered why youtube is so full of videos of quantum mechanics and relativity yet in-depth teachable grade videos are near impossible to find? Because it's so f***ing tedious and boring. Academics should be decided by importance, not popularity.

@trenttagestad5282

4 жыл бұрын

@@dr_arcula k

We need a supercut of Numberphile videos that is just a series of all the times someone references Euler. Maybe another collab with Boyinaband to turn it into something musical.

delightful. thank you. your videos are a gift to the world and fill me with hope knowing people like you and these academicians are out there doing what you all do. thanks again.

"Overloading of a word" found the programmer 😅

@Nobody-Nowhere-Nothing

4 жыл бұрын

I was thinking it was a reference to chess

@EricAtRandom

4 жыл бұрын

That's funny! I had the same thought in reverse. I thought, "Oh, was that a mathematical term that programming languages adopted?"

@Bliss467

4 жыл бұрын

@@EricAtRandom programming is just math but typed. Computer science is just a kind of math. Here, I'll name three things, tell me which of the fields it belongs to: * Numbers * Functions * Variables

@EricAtRandom

4 жыл бұрын

@@Bliss467 That's always my response to people who say they've never needed algebra after high school ... I deal with algebra every single day and I am *not* (directly, at least) a mathematician!

@Dancindazed

4 жыл бұрын

you guys, overloading is just regular english. It's not specialized jargon, it can be used in any field/industry/what-have-you.

When she started drawing them I got traumatic flashbacks of tree(3)

@rcb3921

4 жыл бұрын

Did you take a pass on tree(graham's) ?

@Bluedragon2513

4 жыл бұрын

@@rcb3921 Sorry, I blanked out for a moment. Did you say something per chance?

@nowonmetube

4 жыл бұрын

So you weren't amazed? What's your problem? Brain function overload? Not enough space for input?

@WTFAnimatonsHD

3 жыл бұрын

@@rcb3921 tree(tree(3))

@Astromath

2 жыл бұрын

@@WTFAnimatonsHD RAYO(TREE(G64))

This is perfect timing. Watching this litterally 1 hour before i'm going to learn this in my Discrete Mathematics lecture.

@coffoetmp6925

4 жыл бұрын

"it's a miracle"

@rylaczero3740

4 жыл бұрын

We had a separate subject dedicated to Graph Theory.

@stapler942

4 жыл бұрын

I think my class is getting there soon.

@hrishikeshathalye191

4 жыл бұрын

Exactly the case with me lol. Just an hour before graph theory class.

Was just getting curious about graph theory! Really great talk by the professor!

6:52 I swear there's an Euler's formula in every scientific topic ever...

@JM-us3fr

4 жыл бұрын

Basically. We should start numbering them.

@probablyabsent326

4 жыл бұрын

The generally accepted naming convention for things in mathematics is that theyre named after the first person to discover them after Euler did

@ditzfough

4 жыл бұрын

@@probablyabsent326 i laughed at this harder than i should have

@nowonmetube

4 жыл бұрын

Or is there? 🤨

@ditzfough

4 жыл бұрын

This is why we need a meme of ben stein from ferris buelers day off. Saying euler? Euler? .....

Wow! This is so cool!!! This is a great way to think of the planar symmetries.

Happy Birthday, Numberphile!

This is exactly what we've been working on in my discrete math class for the last 3 weeks.

Have a discrete math exam in a week so this is nice. Thanks!

Great video! Just finished planarity in my 4th year graph theory course.

We're learning this in discrete math right now, super cool

Awesome video! Planar graphs are really interesting. 👍

2:28 Hipity Hopity Does this graph have this property?

I think the theorem around 13:55 is supposed to say "G is a planar graph and..."

@MrDowntownjbrown

4 жыл бұрын

+1. As a test, it is probably more straightforward to think of the contrapositive of the theorem: If E > 2V-4 (where V>=3) and there are no triangles, then the graph is not planar.

@godfryopa339

4 жыл бұрын

You're exactly right I've checked!

learning some of the things on this channel while in a lower level us math class is absolutely phenomenal... i dont understand it all but boy do i try to.. it seems like magic how simple//complex some if these things are and you can tell how completely the person presenting understands them and its mind boggling

A while ago i found a game, called "untangle" (the main story is to free a kite, that is stuck in a tree), where the player has to untangle a mesh of vertices, that no lines are intersected without being connected to a vertex at this point. There are multiple levele, where these mashes should display tangled parts of the kitestring. Actually it´s taking a scrambled graph and transform it into a planar projection.

Oooooo, graph theory! :D A surprisingly useful and beautiful branch of mathematics.

Awesome into and overview of the topic.

numberphile is such a good channel

Nice to see world class expert on graphs here

I love your videos, now taking discrete math course in Taiwan.

that comment @ 12:27 was so insightful

It's like understanding ordered stack action.💚

Is Prof Chudnovsky related to the Chudnovsky brothers (of Chudnovsky Algorithm Fame)?

Finally some graph theory. More!

Happy 8th birthday Numberphile!

Thought i was going to sleep Time to learn boys

@ElTurbinado

4 жыл бұрын

how do you learn a boy

@UnderscoreZeroLP

4 жыл бұрын

time to fail no nut November

You should do a whole follow-up video on Robertson-Seymour theory! And with the SSCG function, you can tie it in with TREE(3) too. 🙂

keep the good work going Brady

Glad to know which occult you like.

What a beautiful video, so elegantly interviewed and helpfully explained.

Teach me more about graphs and embeddings!

really nice animations

I’ve played a few games on the App Store about “untangling” strings, might be interesting for those looking to play with planar figures.

@PunkSage

2 жыл бұрын

One of those games is called Planarity

This is also a game: Untangle from Simon Tatham's portable puzzle collection

Please talk about the laplacian of a graph 😍 that would be rly cool 🤙🏼

Last time I was this early Euclid was still thinking about his postulates

@Jacquobite

4 жыл бұрын

I'm not sure why that sounds so dirty. Maybe Euclid explain it.

@AexisRai

4 жыл бұрын

@@Jacquobite underrated joke

I liked the respectful questions , unusual in modern times

I was working on transition-metal complexes that had a non-planar graph in its base structure a couple of years ago. My former Prof. really wanted to coin the term Kuratowski-complexes for these kinds of complexes.

Seems like something to keep in mind when planning PCB layout

@codecrafter151

4 жыл бұрын

But I believe that it is to much information to compute, if you have more than one copper layer. Because then we don't have planar graphs...

@LouesSCat

4 жыл бұрын

@@codecrafter151 having only just found out about this I cant be sure, but as far as I can see you only need to make sure that each individual layer contains no non planar graphs. I'd have to try finding more information about it to see how 'easy' it is though

Thank you.

The last graph doesn't seem so cheaty if you think about something like a subway map. Only five stations in the city center are densely connected and most stations are only along one route, but that is enough that you can't build it without expensive crossing tunnels.

@Trockenshampooleopard

4 жыл бұрын

Do you know Matt Parker's video about the Tube Knot in London?

The only channel i subscribed only by watching one video

Interesting topic.

In portuguese we have different names for those 2 kinds of graph. The one with x and y coordinates is a gráfico. The other is a grafo

Lets draw 20 million tree graphs All tree graphs are planar graph

@nowonmetube

4 жыл бұрын

Why only 20 million? Why not ALL LOL

That's my professor!

literally what i am learning in university now!

@brunogallego7507

4 жыл бұрын

It's pretty useless...what you gonna use this for?

@joshgomes5939

4 жыл бұрын

@@brunogallego7507 Graph theory is very useful in certain sectors of computer science and linguistics

@cubicardi8011

4 жыл бұрын

@@brunogallego7507 That's not what maths is about...​ People​ like​ galois​ also didn't find a use for group theory, years later people found huge practical potential in that

@kermitthealmighty8355

4 жыл бұрын

@@brunogallego7507 Graph Theory has a wide range of applications and it forms the foundation for many algorithms in computer science. Look up the 'Koenigsberg Bridge Problem'

yessss

What a charming explanation 😍

The first square of 2 is 4. Higher power may be used. 3 and 5 adjacent. If you need higher Dimensions.

Really niceeeeeeeeee!

love the brown paper being taped up on the wall like a whiteboard but it's over a real whiteboard

Nitpick just so students watching this don't get lost looking at some other source: around 12:50 when it's said that V is the # of verts and E is the # of edges, this is not standard. V is the set of vertices, and E is the set of edges. |V| is then the cardinality (size) of the set V (i.e. the number of vertices) and |E| is the cardinality of the set E.

that instrument at the wall is Rababa or Rebaba it is an old Arabic one string instrument :)

Thats so cool

I wonder if there's going to be a special video when Numberphile hits 3.14... million subscribers?

"Those houses are actual houses, they're not these houses?"

At 13:54 it should be "If G *is* planar and has no triangles, then E

8:28 bruh

@JorgetePanete

4 жыл бұрын

🅱️RUH MOMENT

I really like that you clearly know what a graph is (I've been watching this channel for a while, I'm sure you've heard of graphs). But you can still ask good, basic questions, so that your guest can give their explanations. Also, is it just me or does Leonard Euler's face looks a little bit like Matt Parker's ?

@esquilax5563

4 жыл бұрын

You can tell when he gets to questions he really doesn't know, because he finds the answers cool 😁

Very nice

Thanks for your nice lecture, is the empty graph (graph with no edges) a planner graph?

i already watched the entire video. top that!

@flowerwithamachinegun2692

4 жыл бұрын

Physically impossible!

@sigggo

4 жыл бұрын

Lol

@jimdestiny7609

4 жыл бұрын

I can't top that but I can say you are cute. That is all,I'm leaving now.Have a nice day.

@user-ux2ho6ps7j

4 жыл бұрын

Bloke with a female profile...

@collinferreira9706

4 жыл бұрын

@@jimdestiny7609 you fell for the simplest of traps

It took me around 5 min to understand what's going on, but now that I get it, it's actually very interesting.

cool!

at 14:30 a perhaps better way of saying it would be: if you pick any three vertices of a K3,3 graph at least 2 of those vertices must come from the same side and therefore have no edge connecting them

@dynodeath5430

4 жыл бұрын

Therefor its a P3L3

I went through my algorithms class in college three times and no one explained this concept as simply as this video.

This is important for cartography

Make a video on langlands program

Learning basic graph theory for a tutoring interview... I got a notification for this video that just happened to be released today literally the same minute I started learning about planar graphs.

The theorem saying for a planar graph, E ≤ 3V-6 apparently needs clarification since while the graph K2(two vertices joined together by one edge) is planar, the equation does not hold for this graph as shown here: 1 ≤ 3(2)-6 1 ≤ 0 (Not True)

@eclisseriflessa

4 жыл бұрын

V should be at least 3

It is oddly satisfying to know that a pentacle is non-planar.

This is a mix of four color theorem, tree3, the utility mug, and knot theorem

The 3 houses and 3 utilities reminds me of a 3b1b video where you show it's embeddable on a torus

@upliftingcommunity2465

4 жыл бұрын

Lulu Azhal wouldn’t it being on a Torus mean it’s not in a plane? By definition of a plane?

We called a "graph" of a function on a Cartesian coordinate system for example a plot when I was in school many years ago.

The K3,3 graph can be embedded on a torus. What surface can the K5 be embedded in?

@frankstevenson5013

4 жыл бұрын

Sphere ?

@daklhs6460

4 жыл бұрын

@@frankstevenson5013 Nop, a 🍩.

@tomkerruish2982

4 жыл бұрын

Also a Möbius strip. In fact, you can put K_6 on a Möbius strip and K_7 on a torus.

@prosfilaes

4 жыл бұрын

@@frankstevenson5013 For any (finite?) graph on a sphere, find a blank spot and "pop" the sphere. You can map the rest to a plane, with the distortion being irrelevant in a graph sense.

@Maxvr9999

4 жыл бұрын

For every n there exists a g so that Kn is embeddable in Fg, n and g being natural numbers. Same for Fg'. As Tom Kerruish said, even the K7 is embeddable into a Torus (F1). The K8 is not. If you take three edges out of K8, that form a triangle, the graph you get is a minimal non embeddable graph for the Torus. So taking away one more edge will allow for an embedding. The Torus has alot more minimal Graphs. Not just two, like the 2-sphere or R^2.

It feels like there should be some connection between planar graph theory and origami/folding.

I think this is a cool topic in graph theory, and probably relevant to some real world problems ( a guess.)

👑

Lost me (it's late here) at 1:00 min but I was kept entertained by her and the questioning. 👍

If I were to guess, this decimal is a representation of 2^x's many products

Omg i just happened to have a test in Graph Theory tomorrow lol😅

I can see how planar graphs would have many practical applications. Imagine a PCB with components soldered on like capacitors, resistors, transistors, etc. Copper lanes need to connect various components but the lanes are not allowed to intersect.

Now, the K3,3 graph, I remember this. My Question is : Why only take advantage on 1 side of the plane? If you use Both sides of the plane it is solvable (via a tunnel, or on circuit boards it's called a 'via'). The bridge to terabithia..

With the Pentagon graph, try using a torus

Any good video game geometry is able to be drawn as an embeddable graph. Otherwise, you would have a hard time flattening it out to apply a texture to it.

In the theorem at 12:58 shouldn't it say "G *is* planar" ?

Decision maths has never been so accessible. If only I had this a few years ago

@keestv3116

4 жыл бұрын

James Blenkinsopp it's never too late, at least this is what I tell myself.