Four Utilities Puzzle (and how to ruin a bagel)
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- Опубліковано 11 лип 2018
- A new take on a classic.
In response to this collab: • Why this puzzle is imp...
"Topology Joke": • Topology joke
Susan Goldstine's bead crochet video: • Bead Crochet Demo--Sev...
Susan has also collected a page of other artistic renditions of the 7-color torus and links to instructions for beadwork, fiber arts, and other further reading: faculty.smcm.edu/sgoldstine/to...
This video not sponsored by or affiliated with mathsgear, but here's where they sell the official version of the mug: mathsgear.co.uk/products/util...
This video is supported by viewers like you on Patreon! Thank you especially to Caleb Wright, Albert Wenger, Pat Devlin, Jack Heidrick, David Perryman, Jade Bilkey, Chris Pierik, Donald "Chronos" King, Andew Romaner, Jodi Vezzetti, Carol Ghiorsi Hart, Andrea Di Biagio, Charley Sheets, Yana Chernobilsky, David A Smith, and Michael Tiemann!
Oh, and we put in the order for the Tau Day shirts, but we ordered some extra so here's a link to shirts and hopefully your size is still available! store.dftba.com/collections/v... - Розваги
"Oh, that's a nice little theorem you have. It would be a shame if someone were to generalize it."
HalfBlindPrince ok
@@DillyRed k
sheng shu ok
MayMayYt ツ ok
Bunnies Rule ok
If you're going to bagel it, then really bagel it. There are places that make rainbow bagels by weaving colored dough. You could turn that into an edible version.
Sam I'm a simple person who also doesn't care or mind to ingest a few toxins so I would still eat that bagel. I mean it most likely won't kill me right after eating it and I have to die anyway but not eating would still probably kill me faster
DieAlteistwiederda Sharpie ink is supposed to be non-toxic, so you'd probably be fine. It might taste like you're chewing on a big, squishy aspirin, but at least it won't kill you.
Noel Goetowski thank you for this little bit of extra knowledge. We don't have the sharpie brand over here and what we have is toxic so I just assumed that these markers are as well. Well, now I know that I probably wouldn't die much faster than we all already are if I ever fly over to the US and eat a bagel that someone colored in with a sharpie. 😂
DieAlteistwiederda Yes, that is useful knowledge.
Ezekiels Pretzels
The fact that I can understand this, to a degree, even with ten years of medical issues and brain surgeries destroying my memory and fogging my thought process, is impressive. You make a really good teacher, even though my heart broke when you drew on the peach rings.
I died a little inside when the sharpie hit peach ring
Hope you are feeling better :)
I hope you get better. And yes, if all teachers were as good as her learning would be much easier.
how are you doing now?
@Costumed Creeper Better, thank you! Still have some physical difficulties, but the combination of video games and writing fiction have helped with memory and focus issues.
I used to just watch your videos because I liked the art but now I'm actually going to learn about this stuff so it's helpful. So thank you.
All this info is too complicated for my stupid snake of a brain, but her voice makes me feel nice :D
@@toadsoup7507 very true words
Everyone's upset about the bagel, I'm here crying about the sugary goodness that was 4:20.
Same
same
mood
Finally someone gets our pain.
420 :))) but why do i think about the sharingan whe puts the 3 dots on the sour gummy donuts and connects them
Its fascinating how many ways you find to somehow involve food into your video.
Rapophie Cuz they got the munchies. Why do you think they’re so crazy?
Nice avatar, Commander.
never forget the hexaflexamexagon
That’s it! Math= FOOD NO WONDER IM FAT AND GOOD AT MATH!
Can I just say I love that you saw a problem and your first instinct was "how do I make it harder"
(I mean yes I know you're using proven results to work your way down, but still)
1900: “I bet there’ll be flying cars in the future”
2019: “Let’s do some puzzles with a bagel”
Absolutely better than flying cars
@@noxfortes Can't agree more
Flying cars do exist, they are called helicopters.
*Vihart - the only youtuber that you can go to to draw on mugs and bagels*
Finally I've been looking everywhere for a non adult method to ruin a bagel
Is this a subtle advertisement for your new mug merch?
Oh hey again
Either you watch every video on the internet or just the same ones as me and I'm not sure which is more unlikely
+bred From what I've heard, he just *comments* on lots of videos, which isn't the same as watching them all.
Hi neighbour
Yustin I didn't see you in a couple channels dunno why people hate on you :v
Even though I'm older than I used to be when I found vihart I still have no idea what she's talking about
I just like listening to her rambles
Interesting sentence... Will you ever not be older than you used to be, I wonder?
All I know is that I'm getting old for my age.
today i feel like being a bit older
Pielover1617 is a hairry leg world is fool of smart asses
I live how you talk, and how you say your thoughts...for some reason it makes me calm...my friends tell me that "That's weird, but that's why we are friends" but why is that weird....I just like hearing you talk! Keep up the amazing work!!!!!!!!!!
It took about 1.5 sheets of graph paper, and some distractions, but I graphed a 6 simplex on a 8*14 grid, looping around top and bottom. Seeing as I have no bagel or mug to ruin, I will leave the 4 houses and 3 utility buildings in their neat, evenly spaced row in the middle.
On the 8*14 grid picking a row along the 14 axis and spreading utilities and houses spaced along intervals of 2. I drew lines with slopes of 2 and 4/3 and continued them through the connected borders of the rectangle.
I can't believe such a simple solution took me so long, but I am glad I spent the time. This is why I watch vihart and 3blue1brown, it helps me keep these topics near the surface of my mind.
Whoa, never would’ve thought the color-map theory had that kind of a connection to graph theory.
Woah indeed
i love the bridge you drew for the reductions into 4 color map theorem! it's so beautiful
"it gets squished when you do topology to it."
R.I.P. bagel, but quite an interesting method to reach the solution
Well, at least she didn't do that to a Montreal bagel. That would be truly tragic
TheMaskedDonut True
Never mind the bagel.... The candy, she spoiled the candy!
Rest in pepperonis
Oh yay I was waiting for a new Vi Hart video since I just finished reading a Martin Gardner book.
Since Martin Gardner retired, and subsequently died, people like Vi Hart, Henry Segerman and Brady Haran have kept recreational mathematics going.
The good side of youtube
Might be worth mentioning that after you add your internet & secure network, you have the complete graph K_6. Not just theoretical, this actually has some bearing on the puzzle: You have all the simple edges that you can ever have. Even if you added 1000 more types of network, but no more houses and utilities, the puzzle would still be soluble, if not easy to physically draw.
3 VIDEOS IN A MONTH?! I AM LEGITIMATELY IMPRESSED!
I like how I heard about every topic in this video, yet you created your own problem, and used these facts to do something I never heard of before.
This is genius, I watched the original collab video and your method is so much more elegant. Love it!
Words cannot express how much I love you Vi! But numbers can! I love you TAU
It's so sad that you missed that collab. You didn't just solve this puzzle. You obliterated it into tiny little pieces.
I have routinely come back to your videos year after year since about 3rd grade, and now I’m in ninth. Every time I learn something new or relearned what I forgot. Thank you for making math so fun and inspiring me to keep trying with it.
I don’t understand anything you say and yet I’m still subscribed to this channel.
This is absolutely incredible. I am always in awe of the way your brain works and it’s inspiring.
Two of my favorite branches of Maths in a single video! Always fun and informative videos.
Using bagels and mugs is certainly a creative way to solve it; including internet is also interesting. I love how all your videos holds up suspension of disbelief so well :D
Mic drop
Bagel drop
Mug drop
Sharpie drop
AJFes12 +
Bass drop?
Did you see my bag?
Sharpie drop OK. Mug drop might be a bit messy though.
The Masked Performer it's hella trophies and it's hella thick.
You are my new favourite UA-camr forever. I cannot stop watching your videos. They are amazing and you are amazing. And thank you
I've been watching your videos since I started middle school and now I've graduated ♡ you're so brilliant
I got lost in the middle, but when you drew the lines on the handle I had alightbulb moment! Thank you Vi for another great video.
I'm not sure why I subscribed, but I think it's because these videos are oddly mesmerizing.
Math isn’t limited to a flat space so I love how you did this
You are so unbelievably brilliant. I haven't taken a math class in years and still enjoy your videos. I was wondering if you'd ever want to make another video about music theory? I have watched your Twelve Tones video countless times since I discovered it my sophomore year of school. It sparked my interest in theory, specifically 20th century theory, which has grown to be a deep love. I'm a music major now and your video really helped me in my theory 4 class. It helped a lot with 12-tone composition and helped give me a strong foundation in these concepts that made the material easier to learn. I'm now a tutor/grader for my theory professor and I think I owe you thanks for that, but mostly for helping me fall in love with theory ❤️
Did she just destroyed everyone in the original video?
No, they are okay.
Felipe Hindi r/whooosh
Yes
@@Sci0927 actually you got whooshed
Genius, interesting solution! Thanks for your videos Vi!
**eating donut**
dude, you’re _eating my mug_
Your videos make me feel really smart and yet so confused at the same time.
I looooove this puzzle. The whole world is transformed when you imagine space as a torus. Please, please make more torus puzzles or come visit my school and do some torus puzzles with me!
So, does the axioms available to you for doing this math create some sort of topology that could describe the number of valid ways to connect the 7 colour torus problem to the utilities and houses on a mug with internet problem?
Joshua Hillerup I have no idea what you just said. I suck at math
Tropical 24 if it helps what I said basically has nothing to do with multiplying numbers and whatnot. Basically math is one big logic puzzle, or rather a collection of logic puzzles, and a given puzzle could be described as having a "shape".
Exactly what I was wondering 😶
I think what you're asking is "how many ways are there to do this?"
First you need to define what it means for two ways to be different. The most natural way I think is a homotopy, where two ways are the same if you can continuously deform one into the other (i.e. you can "slide around the lines").
Then, the answer is infinite, because any time you use the handle, you could wrap around it as many times as you like which produce homotopicly inequivalent solutions.
if theres an internet problem then nothing is possible
I'm gonna cry, I love Vihart, I love math, the world is a beautiful place
This is really awesome! I felt smart discovering the solution to the mug puzzle in 3Blue1Brown's video but this one really tops the other one.
Wow! Your not dead! I love your videos!!!
I have an intense physiological hunger response to peach rings, and seeing you put sharpie on them was so painful. But for math!!! And entertainment!!! Great video
I recently acquired a copy of Robin Wilson's Four Colors Suffice and so I was excited to see the map problem introduced :D
Nice to hear from you again, Vi 😁
OMG YOU’RE BACK YESSSSSS!
vi you're too smart i gave up understanding halfway and ate a bagel. it was a yummy bagel. thank you vi :)
When you spiraled the 3 utilities around the mug handle, my brain broke. Bravo, well done.
This was so iconic like every single one of your videos is iconic and I love being a mathematician bc we think in this kinda way
Really impressive! And really well explained! Thanks!
I’m going into 7th grade so I haven’t really used the information in your videos yet, but they’re just so interesting to me for some reason that I can’t stop watching :)
This is so cool! youre awesome vihart :’
So before seeing your solution, I did manage to find one, it required about thirty minutes of scribbling with a marker on a handy not sentimentally important mug, and some stories about rebel houses who don't want their wires to play by your rules, but I found one!
Great video! When i saw the original mug video, my solution was to cram as many lines on the handle as possible and ended up with a solution like this!
Please continue the Doodling In Math Class series! I found the dragon one when I was 7 and was actually interested in the math because of the fun way you portrayed it! I will support you no matter what but I just really miss that series
YES! I understood for years that there was a topology solution behind this puzzle but the paper and mug applications always seemed too messy to cooperate with theory. Time to google 4 color map theorem and 7 color map theorem and have this solution cemented in my memory.
Using the 7 color theorem was absolute genius.
Thank you you helped me get better and start to like math so I went from failing to getting an A and liking math ❤️
Ayyy Vi uploaded!
this is the most "hard math" vi hart video imo and I'm really digging it
DARN! That was amazing!
Yay, new Vihart video!
Hey vihart. Here’s something you might find useful. You can wash sharpie off of things using sunblock. Not the spray-on kind, but the stuff that squirts out of a bottle. No idea why. My family discovered this by accident a long time ago. I don’t know if it works with all sunblocks.
Definitely the most aesthetically pleasing solution
This channel just blows my mind...
amazing video as always
You the best! Thanks Vi!
Serious maths here. You never disappoint me.
Finding out Vihart wasn't able to participate in that 3b1b video is like going to see Chicago in concert and then finding out one of the horns players was sick.
Funny though I was subscribed to most of the math channel you mentioned, but only hsve stayed here I guess I like the drawing or your delivery more.
Man! I just discovered your channel and I am hooked!
Your mind is so beautiful and goofy.
I think I am getting inappropriately attracted to your brain.
this is so awesome you’re my hero
I don't understand half of what you're saying, but I'm still facinated all the way to the end
What reason does this have to for some reason become one of my favorite channels
Ha! I took a topology course from Gerhard Ringel and at one point I painted a bagel with 7 colors to prove that the graph was embeddable in the torus. I called it "embagelable" which gave him a chuckle. No idea what became of the bagel.
That poor markered bagel.Its valiant sacrifice for Math shall not be forgotten.
I love puzzles !!!, this one was a fun one, too.
You’re so cool this is the reason I subscribe 👏👏
I can never avoid commenting on a bagel video. That bagel's not ruined, it's a work of art!
OMG FINALLYYYYY A VID!!!!
I love this, not because I love math, but because I love being reminded that problems that seem impossible might not be.
I'm 11, yet I still watch your videos.
I think Vihart wins this round of educational UA-camr challenges. excelent video.
please come up with a clever challenge/merch concept so i can buy them as mathsy christmas gifts =D
especially as gifts to math teachers.
Wait! I thought this was completely unrelated to me and I was just watching a fun video I didn’t understand but made me feel smart
But then I realized this directly correlates to my job and is very familiar!
I make 3D models, and 3D models are made up of faces. Kind of like papercraft.
However there are rules. Like, usually you can only have triangles OR four sided polygons. And you have to make sure certain edges are clean, forming nice loops all around the object. You don’t want to have the edge of a cube cross through the middle of a flat face
So you’re always ending up with these stray edges that don’t go anywhere. All you desperately want is to stick it on a vertices
And sometimes the only vertices that makes sense is one you can’t reach, unless you snake all over the object and find it on the other side
That part where the three lines are crossing over the handle side-by-side? Even though they started as being far apart?
Very familiar!
Loved your video :DDD (as usual)
Nice challenge at the end, I finally got it. To get the complete planar 7-graph on a torus, start with the complete 6-graph on a torus:
/ / /
- A-B-C-
/| /| /|/
-1-2-3-
/ / /
Now take out the three edges in the middle of the box:
/ / /
- A-B-C-
/| |/
-1-2-3-
/ / /
Replace them with an X connected to all six:
/ / /
- A-B-C-
/|\ | /|
| X | /
| /|\ |/
-1-2-3-
/ / /
Now we just need to replace those three edges from before. Add 2-B by
going straight top to bottom. Then add 2-C adjacent to 1-C, and 1-B also
adjacent to 1-C. Looks something like:
/ |// //
- A-B-C-
/|\ | /|
| X | /
|/ | \|/
-1-2-3-
// //|/
Translated to a coffee mug, that's six edges sharing the handle!
Thank you for this explanation. I know this is a bit late, but I think your diagrams omitted the A-3 edge. Regardless, they were very helpful for visualizing the solution.
@@davidsarea51 You're right! Fixed. :)
Wasn't expecting such a prompt and polite response. Color me impressed. You rock!
You have a very cute mind. In a very good sense. Your videos are such a pleasure (especially the Pi/Tau series) :)
Who knew math and theorems were so artistic and fun
I saw this problem on brilliant while working through one of the weekly challenges.
It didn't mention the house and the utilities though, it just used vertices. But it's just the same thing.
I was simpler with the 3 utilities challenge, I simply bundled the 3 lines next to each other and had them pass through the houses in a straight line and return back to the utilities.
Nobody told me that was forbidden. The only rule was that you're not allowed to cross them and bundling them was never forbidden yet people seem to easily forget that. The thing is, people think that the houses are single dots that you can only touch from one side but I treated them like boxes through which lines can be drawn. If you use this method you can solve the entire problem without any hassle at all. You just get a nice 3 color road going from the utlities to the houses and back.
The internet would probably be harder BUT I'm sure I'd find a way. Nature always finds a way.
hey vihart! if you want to keep the mug washable, you can bake on some oil based sharpie ink in the oven.
I was the topology person when I first saw 3blue1brown's videos. I immediately thought of the joke and realised there was no reason why Grant would put it on a mug unless I were meant to model it as a torus.
Aye! Your back.
(3:00) "In case your into mathematical beadwork..." Hilarious. I love it.
That was really interesting!!
This was fun to watch while eating!