Can you solve THE Klein Bottle Rubik's cube?
ฝัง
- เผยแพร่เมื่อ 7 ต.ค. 2016
- In this video I tell you about Klein bottle Rubik’s cubes, Torus Rubik's Cubes and Klein Quadric Rubik's cubes as an introduction to a whole new universe of twisty puzzles.
Get your own Klein bottle Rubik’s cube, as well as more than 800 other topological twisty puzzles by downloading the free incredibly powerful Rubik’s cube simulator MagicTile by Roice Nelson: roice3.org/magictile
Be one of the select few to get your name recorded in our limited edition Mathologer "Klein bottle Rubik Cube Hall of Fame" by solving the tricky puzzle and following this link: roice3.org/magictile/mathologer
To get some help with this challenge check out the second part of this video on Mathologer 2 in which I talk about the MagicTile interface, show you how to design and record algorithms as macro moves, as well as talk you through a complete solution of one of the easy Harlequin edge-turning puzzles (featuring the all-time simplest three-piece cycle algorithm as well as some cute parity problems): • Intro to MagicTile (Pa...
Also check out the following videos for more background information.
"A simple trick to design your own solutions to Rubik’s cubes": • A simple trick to desi...
(for an introduction to designing your own algorithms for solving twisty puzzles)
A mirror paradox, Klein bottles and Rubik's cubes: • A mirror paradox, Klei...
(An introduction to what Klein bottles are all about and a bit of fun with putting Rubik’s cubes INTO Klein bottles.)
Cracking the 4D Rubik's Cube with simple 3D tricks: • Cracking the 4D Rubik'...
(Your next challenge after the the Klein Bottle Rubik's cube. Another hall of fame awaits.)
Klein Quadric II: • The Klein quartic
An animation by Jos Leys that shows how the Klein Quadric gets glued together from the patch of 24 regular 7-gons in the hyperbolic plane.
Enjoy :)
Burkard
![[FULL EP.13] เซียนหรั่ง พา ไททศมิตร ลงเรือฝึกสกิลหว่านแห | เฮ็ดอย่างเซียนหรั่ง | One Playground](http://i.ytimg.com/vi/EWFuf2Av0K0/mqdefault.jpg)
Solved it just now, I created a single corner rotate algorithm that takes 396 turns and it helped a lot because most algorithms don't work on every tile you click. You have to put a tile in a very specific place for them to work or otherwise you get very unpredictable results!
Great, congratulations :)
Thirteen people who managed to solve the Klein bottle Rubik's cube so far (and thereby earned the Mathologer seal of approval). A quick reminder, if you've solved the puzzle submit your log file here to get your name recorded in the Hall of Fame: roice3.org/magictile/mathologer/
Just solved it, hopefully #14! Cheers!
That's great. We'll find out next time Roice updates the leaderboard :)
We're up to 29 now. I'm working my own solution so I can get onto the list before it fills up! I've never solved it before and am hitting some fun, unexpected configurations.
I just started into it.... holy cow. I had been just working it intuitively. But I forgot that when the pieces cross the top/bottom margin they become mirror images of themselves. Delightfully challenging.
Any suggestions on # of rotations for a scramble?
Charles Coslor, even though it is likely overkill, I'd just go ahead and do the max offered of 5000. Glad you are enjoying it!
I downloaded the program but unfortunately my graphics card is too old to run it. It seems like going into the 4th dimension is really resource intensive.
"We cannot predict where, ultimately, the Computer Revolution will take
us. All we know for certain is that, when we finally get there, we
won't have enough RAM."
- Dave Barry
Maybe one day they'll support vec4's and 4D matrix transformations.
my antivirus had to be convinced its not a virus lol
they actually do. for example, a vec4 is sometimes used to represent a color with red, green, blue, and alpha (transparency) fractions.
Pledge yourself to the Great Old Ones, and you shall receive a superior graphics card from their superior dimension.
Finally a twisty puzzle for us 4 dimensional beings.
For years I've admired the properties of your 3 dimensional twisty puzzles, but lacked the resources to expand them into our 4th dimension. Thanks for this!
Ur welcome.
Btw a 5d friend of mine needed your 4d help in a 5d rubiks cube. :)
CaHOOTS can you tell your 5d friend to make a Rubix cube for us 6d beings? It would be greatly appreciated.
3D being here. My friend who's a 7D being looks down on this conversation with shameful laughing, and wants a seven-dimensional rubik's cube.
My masters have come at last! I am Rasputin, your humble servant, here to do your bidding, oh Great Ones! Say the word and I shall initiate the link between our dimensions! We shall change the world!
Pleaee give me a 127 dimensional cube, all of your cubes look like dots to me so please help
Hell. I can't even solve a fucking regular 3x3x3 rubik's cube, and I am watching a video about a Klein Bottle Rubik's cube. What am I thinking?
"Hm, this looks interesting... and confusing."
Could be. However, for now, I am just in a "Nope-Nope-Nope-Nope-Nope-Nope-Nope-Nope-Nope-*SO-MUCH-NOPE*" state, while fathoming that if I have to solve this abomination in the future, then you can find me making death wish.
If you can't solve a 3x3x3 then ask someone or look it up unless you want to figure it out for yourself
CDA3000 I did look it up several times. Somehow my brain just refused to remember how to solve it.
You shouldn't teach it to your brain, you should teach it to your fingers. Remembering those algorithms is more muscle memory.
This is probably the nerdiest thing I have ever seen… AND IT'S AWESOME :D
You must be new to this channel. Check out some of the other videos :)
Instead of calling it Klein bottle Rubik's cube
Isn't it better to say Rubik's Klein bottle XD
Erno Rubik and/or any other Rubik has had little to nothing to do with this invention. but it closely resembles the heretofore mentioned "Rubik's cube". the "Klein Bottle Rubik's cube" is made of hexagons, and infinite despite repeating. Therefore I believe it should be called The Rubik Inspired Hexagonaly Tessellated Klein Bottle Puzzle.
"The Rubik Inspired Hexagonally Tessellated Klein Bottle"
Bless you
@@thesprakledfrog3435 It is not infinite. It is a finite "folding" of an infinite tesselation of euclidean plane that is covering this "folding". There are several finite versions of it, with various numbers of squares, hexagons or triangles. Similar to the Klein's Quadric "Rubik's Cube" which is also a finite "folding" of an infinite covering tesselation of the hyperbolic plane.
Hey, I got added to the list! It was a really interesting fun solve. I definitely did some double takes when I ran into mirrored corners and single rotated corners. I had to do some hard thinking to fix them. Thanks for showing me the program. The other puzzles are great too.
That's great, congratulations :)
Finally solved it! The bit about moving a piece around a loop to "flip" it was very cool. Not sure I fully understand it still, but fun none the less. I'd love to see more twisty puzzle type challenges in the future too!
Solved! File is emailed in.
This is an AWESOME puzzle. I haven't had this much fun since solving the 5D Cube!
That's great, congratulations. Have you already tried the 4d Rubik's cube? That was one of my twisty puzzle highlights this year :)
Yup! I used to spend hours and hours solving it and resolving it. It was sort of... meditative for me. When I was looking at it I could forget about everything else, and I had so much fun figuring it out.
Wow i didn't expect the corners to flip over
Unfortunately it's not a "real" klein bottle, just the closest we can get to one, because the klein bottle is a fourth dimensional manifold (It doesn't actually intersect itself), but this video is super cool. The Torus one was less cool but also super cool.
EDIT: I forgot to consider the fact that it's a program that can actually have a fourth dimension. I'm dumb ignore me.
why did we never touch topology in school
It's a mystery. A lot of it, like for example Mobius strips and Klein bottles are very accessible and really so much fun :)
arch O
Because it is mostly useless in the real world for most people
The odd thing is why do they teach so many things which fit that description as required classes
Exactly :)
well it's not a practical requirement, but it would be an awesome optional class.
Easy answer: SAT doesnt cover it. Parents doesn't know
guys it's still going there are about 30 places left as of 10/28/16 Us
28/10/16 Everyplace that has a logical date system
"Klein Bottle Rubik's Cube" - because the 4 dimensional Rubik's cube wasn't hard enough.
This one is easier than the 4d one :)
I just solved the Klein bottle cube. I wasn't expecting that parity at the end of the solve, and it was a great pleasure to work it out in the end.
This was a very fun challenge!
Great make sure to send your log file to Roice, details in the description :)
I wonder what a Klein bottle puzzle would look like if you bandaged it...
Hell is what it looks like, hell.
What does bandaged mean in twisty puzzles? I've seen it used frequently but searching for an explanation seems impossible.
It's when you move a piece in a way that makes it so other pieces cannot be moved without moving that piece, or "removing the bandage". It can create some pretty complex puzzles on the more unusual types of cubes.
How did you create this video? I love it.
As of this morning, the challenge hall-of-fame is half way full! 50 folks have solved THE Klein bottle Rubik's cube so far.
roice3.org/magictile/mathologer
What is this? Rubik cube itself is so complicated and you are talking about Rubik cube and Klein bottle together mixed.
My brain blown away...
There arent enough of your videos for how good they are
Wow! I really love the parity cases on the Klein bottle Rubik's puzzle. You can have pairs of corners reflected with respect to the local configuration, as well as rotating a single corner. Of course these two parity cases are related and can both be solved by swapping pairs of pieces over the reflection. It's certainly strange to see a single corner rotated all by itself, having solved so many spherical puzzles.
it is pretty surreal when you see that there is only one corner turned, I thought at first the program messed up during the scramble.
I had this problem too.
DrRawley it'weather clear a pretty simple solution just rotate it once the wrong direction then switch it with a mirrored one then turn it twice switch it back then It's solved.
Not even subbed and found early
Do you like Rubik's cubes or Klein bottles ? :)
Both for sure
don't listen to him.... hes a liar 😲😲😲
I just now noticed this challenge. I had solved the 3X3 back in the 80's without any instructions or tutorials, and then took on any other puzzle that came out. In the past year I got hold of 3 more puzzles and solved those, so I am really looking forward to this challenge
Have fun :) (And once you are finished with this one try your hand at solving the 4d Rubik's cube. That's a really nice challenge.
I'm loving the program. When one of the students in our math resource room was all upset because someone had mixed it on her before she had a chance to analyze the results of specific movements. While she was out I quickly solved the puzzle for her, and as a result the students bought me another puzzle to see if I could analyze and come to a solving solution. Of course the professor for Game Theory decided to mess it and wanted to hear my theories and strategy to solve the puzzle.
Since then I have been given all kinds of puzzles to solve, and I am now ready to find another to add into my growing collection. This program is just making me think of my moves inside out LOL
I finally have a little free time, and have started on the basic cube, playing and working through the puzzle with my now inside out methodology, I have most of it done and I should be able to get that one puzzle finished, and then I will work up to the one that looks like the Megaminx.
Its a rainy day here in Montreal and I'm really excited by that magic tile challenge 😈💪
It's a fairly tough one :)
Which will give you lots of free time to tackle the Mathologer challenge ? :)
Has science gone too far???
Science hasn't gone not too far enough!
i believe science haven't get here yet, is math that gone too far
Noel Goetowski yes they have making human animal hybrids
Someday the piecing together of dissociated knowledge shall open up vast, terrifying vistas of reality...and then the Gateway shall open and They will enter our dimension! You will know madness unlike any other being in the multiverse
I did it!!!
Using the software is a lot easier than real life, because you don't need to memorize any algorithms. You just click the one you want to use and apply it. And finding algorithms is easy with Mathologer's method of solving any cube.
That's great, congratulations :) You are already in our hall of fame ?
#91
Thanks Dr. Eggman for the great video
I have it all solved except for a single rotated corner, and two mirror pieces that I forgot would be mirror when the crossed the border from one side to another, this last layer is definitely tough. I hope the rotated corner will fix itself after I work on fixing the mirrored corners.
I have made algorithms for mirroring two pieces and for rotating single rotated corner.
Use solved bottle for making algorithms, 3 corner cycle from standard cube and some intuition is all you need.
Start macro definition on a piece and press F1 to start Setup moves.
Transfer the piece to the "other side" and press F2 to end setup moves.
Swap the piece with a piece from this side (3 corner cycle), press F3 to undo setup moves and then use reverse 3 corner cycle. That's it, you got two mirrored pieces - save the macro.
Then use this macro on the same spot: macro, rotate right, macro, rotate left, macro, rotate right, macro, rotate left - you have rotated a single piece, create a macro of this.
After understanding how those work, my "mirror two pieces" macro went down from 90 to 30 moves and "single piece rotate" macro went down from 390 to 68 moves, but those are much more complicated to create.:)
4:41 I'd love a tile design like that in my house
Nice video :D
So what is your personnal best with the good old 3x3x3 rubik's cube?
Mine is 16.31 seconds :P
You are way faster than me. I am actually not into speed at all. As far as twisty puzzles are concerned I am mainly interested in collecting the most ingenious ones and designing my own algorithms for them :)
I got a lucky 16.50 some time ago, but I average like 20-21 seconds
I love the video and the software! is there a video/written instructions on how to use its advanced features?
Check out the Mathologer 2 MagicTile video to dig a bit deeper. th-cam.com/video/iOla7WPfCvA/w-d-xo.html
If you still have questions after that, just let us know!
thanks matey! :)
Where is the linux version of the software? Ideally put it in the Ubuntu package repo.
You'll have to ask Roice that, e-mail on the challenge page; see the description for this video :)
I managed to build it from source on linux mint. I had to make some changes for it to work, but nothing major. My changes can be found at github.com/remuladgryta/MagicTile. To build them, you need to have mono and opentk installed. The following commands should do everything for you:
cd && apt-get install mono-complete libopentk-cil-dev && git clone github.com/remuladgryta/MagicTile.git && cd MagicTile/ && xbuild /p:Configuration=Release MagicTile.sln
If everything goes well, you should have an executable at ~/MagicTile/MagicTile/bin/Release/Magictile.exe
How does one get opentk installed so mono will find it?
For some discussion about getting it running with Mono (some folks have been successful), see this:
github.com/roice3/MagicTile/issues/7
Amazing! I had this idea as well after watching your videos! so nice to see that you have dont this
if you get a Klein bottle by following the procedure for transforming a square to a torus but twisting one edge, what happens when you twist both? what happens if you twist them with the same or opposite handedness?
When you twist both you get a projective plane. There are also MagicTile puzzles on the projective plane. However, they don't appear under Euclidean puzzles like the Klein bottle and the torus but under spherical. The reason for this is that when you identify both pairs of opposite edges of a square twisted the resulting geometry does not have the "looks-the-same-everywhere" property that I talk about at the start of the video. You do get this when you identify antipodal points on the sphere. Anyway, I'll talk about all this in another video sometime. The puzzles don't care about handedness since they are really living inside the surface :)
I've been pondering that for a while but I don't know how to search it up.
Excellent video, keep up the good work!
Awesome videos! Klein bottles are AWESOME and it reminds me of wormholes!
I've been looking into projective planes and other spaces a little bit lately. I'd like to hear more about them.
I used to specialise in projective geometry among a few other things, so there will definitely be some videos on this way of doing geometry :)
Cool! Looking forward to them!
Dude, you're the best!
I have to say, the puzzle was really enjoyable to solve! At first it was quite hard to wrap my head around it, but the challenge and some interesting situations surely made an interesting afternoon :)
That's great. Mission accomplished then. Did you send your log file to Roice to have your name recorded in our hall of fame?
Of course! :)
impressive concept ! (Y)
Ps. the cube you showed at 6:19 is curvycopter !
Yes, well spotted :)
Very cool. The colors are wonderful, its like math on art drugs. I once wrote a book about circle puzzles. Always new it was the tip of the iceberg. You can have intersecting cones as well.....
12:34 that moment, when fidget spinners were predicted
Cool ... mind blown. My favorite was the fidget spinner puzzle near the end!
Thirteen people have solved this and i'm just sat here like
*wut*
If you call that hexagonal face puzzle "the" klein bottle Rubik's cube, how about doing similar thing with Jing's Pyraminx and Megaminx? They also have centers, edges, and corners, and they can rotate faces (though Jing's Pyraminx can also rotate corners as corners are opposite faces on a tetrahedron).
Finally! I've read in the yahoo cuber group, that you wanted to make a video about this
Yes, took a bit longer than I thought it would. Did not know much about MagicTile to start with and so it took a bit to solve a couple of the puzzles collected in it to get a good feel for what is possible. Also, MagicTile used to be aimed very much at experts. One of the side-projects was to actually make MagicTile more user-friendly and accessible and as a result the program now looks quite different from two months ago when Roice and I started talking about making these videos :)
Ok, I havn't known that. Thanks anyways!
Yes! MagicTile is much better because of Mathologer's influence!! (and I'm really grateful for it)
why is that sound satisfying when you slide the pin through
Wait... a Klein bottle only has ONE SIDE. The whole damn things should be one color.
That's why the surface is split into squares, just like the cube's surface is split into squares.
It's a generalization. If you think of a rubik's cube not as a six-sided polyhedron,but as a tiling of a sphere with 6 rotating circles of a certain size, each centered on a tile, you can generalize the puzzle to an infinite amount of combinations of tilings (sphere, flat, hyperbolic), circle placement and circle size.
I think it's brilliant.
Are you trolling? Did you not watch the video? And why are so many people upvoting this?
You can color a single surface with multiple colors… For example, think of a beach ball. It has multiple colors on one surface.
Lol, ever heard of a sticker mod.
I have on locked a fear of Rubik's cubes now. Thanks.
I'm not sure that I solved the klein bottle version of magic tile, but I do hold the only spot in the world to solve magic hyperbolic tile's hardest version (52 color). Magic hyperbolic tile is staged in hyperbolic 3 space instead of 2 space. If anybody is interested, I encourage you to google Magic Hyperbolic Tile and give it a try! It's a really awesome program written by the late Andrey Astrelin. Magic Tile is an amazing program as well, and Roice Nelson is awesome for writing it!!
I can't even solve a regular Rubik's cube, a Klein bottle cube is a distant dream haha
Check out this video if you are interested in finding your own algorithms for solving Rubki's cuble like puzzles
th-cam.com/video/-NL76uQOpI0/w-d-xo.html :)
When I see these things I am proud to be hungarian :)
Same :D
serwas! greeting from your neighbor (Austria) ! :)
i am proud to not be tribal about my approbations.
And I'm proud to be a human : )
It's the current year. We say hupeople.
how do you view it not on the plane in the program?
Thanks for the great video and the interesting challenge! It was a lot of fun! The weird effects of the topology almost fooled me in the end...
If you have not done the 4d Rubik's cube yet I suggest you attempt that one next :) th-cam.com/video/yhPH1369OWc/w-d-xo.html
I did that one too, already saw your video!
So glad TH-cam recommended this channel to me. Numbers are amazing. Ooooooo, @Mathologer I wonder if you can work out what Numberwang is (That Mitchell and Webb Look - Numberwang reoccurring game-show skit)
I've gotten it to a point where everything is solved, but one corner is twisted, and I have no Idea where to go from there.
Is your corner twisted on the spot or does it appear reflected (and twisted)? In any case whatever you are looking at comes up because of the way things are glued together. You basically have to take that offending piece on a walk around the Klein bottle. Make sure only this one piece makes a roundtrip, other pieces should only be perturbed slightly and not also complete roundtrips. Probably a good idea to save your partial solve and then to experiment what effect different roundtrips have on your piece when you move in different directions :)
It's not reflected, just twisted. I did make a save at that point, and have tried that "walk it around the klein bottle" method, but I just can't find a way to work that piece into it's rightful place without isolating a different piece from _it's_ rightful place.
Ianwubby Keep in mind that twisting a corner in one direction has the same effect as twisting its mirror in the opposite direction.
MY TWO FAVORITE THINGS TOGETHER
Now, waiting for the real projective plane Rubik’s cube 😎.
*EDIT:* @13:00 Thank you.
Ah, nice to see more crazy puzzles showing up here, I'll be checking back to see people's reactions. Will MHT633 be showing up eventually? That's the weirdest geometry I've solved (in my opinion anyway), it's very cool.
Not sure I am familiar with this puzzle. Is this one part of MagicTile? What makes it so special in your opinion?
It isn't in MagicTile. It's based on the {6,3,3} tiling in H3, a pretty but very confusing geometry, even after being familiar with MagicTile.
Find it here: astr73.narod.ru/M3dHT633/M3dHT633.html
I just realised I never submitted my log file for that one, I solved the smallest one years ago and didn't realise there was a list. I'll dig it out later, and submit my Klein cube solution just now since I realised I'd never solved this one before, it was interesting!
Great, thanks for that, will check it out :)
Another great video as always but your photo of a "helicopter cube" was actually a curvy copter, a real helicopter cube actually consists of 8 triangles on each face
Well, spotted. I've actually got both but somehow the wrong word slipped out :)
People interested in the hyperbolic plane: check out this game called HyperRogue, available on Steam (or for free on Android via the Google Play Store). It's a rogue game except you play it on the hyperbolic plane (instead of a regular grid). Very cool.
Hey! First of all, I recently found out your channel, and quite honestly, I really really enjoy your videos Sir!
So I had a question.. I'm an architecture student and I've been fairly intrigued by Klein bottles lately.. so I was wondering, can the concept of Klein bottles be used to somehow make architectural spaces/forms.. I understand a Klein bottle doesn't really enjoy being in our 3 dimensions :P .. but it's just a thought..
Actually there here in Melbourne where I live somebody has built a Klein bottle house. I once wrote an article about it www.qedcat.com/archive_cleaned/166.html
Woah that's interesting.. Will dig a little deeper into it.. thank you so much!! :D
As an alien having access to the fourth dimension, I do recommend the Rubik's Klein bottle to Rubik's puzzle lovers. It's my favorite hyperdimensional puzzle, the only one that can be used to hold drinks once it's been solved!
When I open the program, the only puzzle I can use is the Start here thing, how do I get other puzzles?
I was thinking, once, of using a hyperbolic plane tiled with octagons as a base for a pocket plane in a D&D game.
And not telling the players.
They'd have a ship with some sort of inertial compass - they could change their direction by one of the cardinal points, but because they are on a hyperbolic plane, the results might not be what they expected : move, right, move, right, move, right, move would not take you back to where you started.
I was concerned about the openness of the hyperbolic plane. The map would have to have bounds, some sort of if you go too far the plane starts to run out. But this video mentions that you can make closed shapes on the tiling - the three hole thing being one of them. This makes a map of tesselating octagons feasible.
-- EDIT --
Come to think of it - you can make a closed space by making a "patch" of octagons of any shape, and gluing the edge to itself … provided that every corner on that glued edge has 3 octagons.
That sounds like a great idea :)
Check out this hyperbolic maze game for some inspiration! It may give you a head start on code too.
www.madore.org/~david/math/hyperbolic-maze.html
my brain is itching..i was happy about the explanation of 4th dimension by Carl Sagan in Cosmos. damn!
Would a snub disphenoid tiling work? I know that half the corners would connect to 4 faces and the other half connect to 5 but surely that would just add to the challenge!
Wouldn't mind trying a puzzle like this myself :)
hmmm, interesting question, and I had to look up what a snub disphenoid even is. I think this won't work in MagicTile because although it is a polyedron with only regular triangular faces, you couldn't tile the sphere with these triangles in their configuration and keep all the tiles regular. The fact that some vertices have four faces attached and others five is an interesting obstacle too.
Perhaps by relaxing the regularity constraint (and possibly other things), workable puzzles of this Johnson solid and others could be created - cool idea to think about.
I think I'll have to solve the standard 3x3x3 cube first... (I want to solve it on my own without looking up algorithms)
palmomki good luck
That's great, make sure to check out this video if you get stuck (even if you watch this video and subsequently manage to solve the 3x3x3 in my books you can claim to have solved it "on your own"): th-cam.com/video/-NL76uQOpI0/w-d-xo.html
I can't solve a flat 3x3...
I've messed with real rubik's cubes a lot, so I'm going crazy over this.
I know it man but the turning is great it never catches
This is pretty cool.Thanks for showing us this.
Just a maybe-dumb question...
Could you possibly show us how a regular Rubik'c Cube looks on one of those diagrams? Because they look and feel like a different kind of puzzle to me.
I'd say just download the program. It's got the normal 3x3x3 and four different ways of looking at it. Maybe also watch the supporting video on Mathologer 2 to find out what is possible in this respect :)
Amazing t-shirt you have. My uncle Marvin was really good at Pacman on Atari back in the day. Us kids used to call him Marvin-man, ha-ha.
I was wondering how you would apply a face of a faceless object to a single plane Until I saw that the plane was in fact infinite. That made more sense. I love experimenting with single face and (theoretically) faceless objects. I find them fascinating and confounding. Nice video btw.
Can you do a video on the question "if two number behave the same, are they the same?"
In the graphic at 3:21 the red/yellow borders are switched!
as soon as i realized the difficulties of moving pieces to the opposite side i audibly screamed.
In the hyperbolic plane puzzle, since you can have any tiling, so regular polygons of any number, could you take the number of sides of the polygon to infinity and have circular tiling, that is faces that are circular?
Bordpie yes but when projecting it onto a 2d surface if im not mistaken it would look like a circle with infinitely many lines coming out from it
Great question. Yes you can have a hyperbolic tiling of "apeirogons", that is tiles with an infinite number of sides. But they are not circles! See this wikipedia page: en.wikipedia.org/wiki/Apeirogon#Apeirogons_in_hyperbolic_plane
MagicTile does not yet support these, but hopefully in the future :)
Multiplication is a macro function of addition.
Division is an inverted macro function of Multiplication. [It breaks at 0]
Subtraction is the addition of negative values.
Negative values when it pertains to reality are similar to imaginary numbers [i]
-5 and 5i have a lot in common when it comes to physical reality. ;)
Yes, but how does this relate to this video? :)
Your videos are good.
Is there a place to see the actual hall of fame yet? So that people in the future can tell if the 100 spots are full already? :D
All in the description: roice3.org/magictile/mathologer/
I saw the link but there were no names, so I wasn't sure if it wan an actual list. I am still working on solving the "last layer" cheers!
where'd you get that T-Shirt? Love it!
Actually I think I got this one from K-Mart :)
I'm almost done, just need to swap two more corners :3
Did it. And there's ... no celebration? I was expecting something :P
I guess it's just like physical cubes.
Congratulations :)
ha! RedsBoneStuff, there's not a lot of fanfare, but it does ding a sound when solved. For some of the really hard puzzles, it should definitely throw a party or something. For now, you'll have to content yourself with having reached a state of Rubik enlightenment :) floatuniverse.com/post/135266053873/via-floathouse-rubixcube-rubix-master
Roice Nelson As I said, just like physical cubes.You solve them, and if there's nobody around to see, you just, I guess, scramble it again.
I just solved the default hyperbolic one. It's even more fun than the klein one!
I am crying from awe. I want to live in the 4th dimension only to get this KleinsRubiccube.
Well, I'd say get started by playing with MagicTile. Definitely one of the coolest Rubik's cube simulator out there :)
OMG this is so easy!
Not hard if you are familiar with making your own solutions, but very challenging for everybody else I would think :) You've sent your log file to Roice ?
I am way too early lol
Great video!
As a suggestion, could you make a video talking more about hyperbolic plane? I've seen a few of those in other channels, talking about the planification, but I never got the feel and hang of it...maybe you could do something linking it to Escher
Yes, a separate video on the hyperbolic geometry is already on of my ever-growing to do list :)
That's awesome, looking forward to it! Hyperbolic geometry seems a bit alien to me, but has lately found many interesting applications (e.g. in the mathematical modeling of networks).
I love Klein bottles.
Can we get hyperbolic puzzles in higher dimensions?
Yes, absolutely, there is also software that features such puzzles. Just follow some of the links in the description :)
i've always wanted to ask you this:
is there any such thing as a physical perfect curve?
the shortest distance between 2 points is a straight line, so you end up with a (x)gon of straight lines. this means a curve would be impossible given the limits of our physical universe, correct?
Pretty much. All of the math we use to describe the real world just gives approximations of the real thing(s) :)
so there really is no circle? just a guess of what one may look like.
i have been bullied over this concept of there being no such thing as a perfect circle. PEOPLE HAVE ACTUALLY HARASSED ME ABOUT THIS hahah
I love your T shirts.
oh my gosh, this is so confusing... WAKE ME UP!
random voice: wake me up inside♪
Me: CAN'T WAKE UP!
12:34 Oh no, not fidget spinner again!!!
How do you represent a normal rubik's cube as a flat square? I have a hard time imagining the two next to each other.
A normal Rubik's cube (or any cube) is topologically equivalent to a sphere, so you cannot cut it and unfold it into a flat square, as you can with toruses and klein bottles.
What you can do is puncture the sphere in a point and stretch the hole until the surface becomes a flat circle. This is shown at 11:26 in the upper left corner, although not for a regular Rubik's cube.
What happens if you link both sets of edges with a twist?
Then you get something called "the real projective plane". You can actually also find puzzles based on this surface in MagicTile. However, you do not get the nicest incarnation of the real projective plane by linking both sets of edges of a square with a twist, you get it by identifying across the boundary of a hemisphere. And so in MagicTile projective plane puzzles show up under spherical puzzles :)
My mind is blown!
Mission accomplished then. Did you already watch the supporting video on Mathologer 2?
Mathologer - No, but I'm getting ready to. I didn't even know about your second channel. I just now subscribed.
Cool, I don't really think of Mathologer 2 as a channel, it's more a place where I can put things that are a bit more specialized or things that did not quite make it into one of the videos on the main channel. Good to have :)
Please, does anyone know how to make a Macro? I've check the page and the starting step is: Start Macro Definition (Ctrl + Alt + Left Click) but I can't press it, it's grey and I can't find a way to do it.
Thanks.
8:05 Wouldn't THE Klein bottle Rubik's cube have 6 faces? As in, make it 2 by 3 hexagons?
very cool
that a great idea it'll be a challange
Hurry up, last time I looked there were not many slots left in the Mathologer hall of fame for this challenge :)