I love topology and a game that allows people to work on spacial visualization and topology, and teaches how to take a slice of an object and reverse engineer a design AND can teach coordinate manipulation like from rectangular to polar form is SICK, please more of this
@@ASaltyAcc that's really easy actually: each transformation is a matrix, multiple transformations is just a matrix multiplication. The desired shape (i.e. an equation with three variables) has a "solution matrix" attached and you compare the two (solution vs. user created). For the general shape you check if certain values are zero, positive or negative and then you just state an error for each of the fields that a user is allowed to be off. 🤷 Rotating or moving the user shape changes the transformation matrix as well of course. I find it more fascinating that we're at a processing power that allows this to be calculated on the fly 😉
I guess the CAD classes I took were worth it because this game seems pretty easy to me so far - not that that makes it any less fun, I absolutely love this one
It's cool to see that his outstanding puzzle solving ability powers through fairly quickly despite not having trained his brain specifically in 3D CAD-type stuff. Learning is cool
@@-NGC-6302- Cause it's nowhere near as complex as you are desperately trying to make it. Kinda seems like you just wanted to tell everyone you took CAD courses.
When he tries to explain a curve he's looking for, he brings out the post it note and bends it the exact same as the last time he was trying to explain a curve, leaving me more confused
After looking it up I've noticed that this is actually a sequel to another game called "Engare", and based on this I think it might be interesting to check out.
@@Phriedah It shows some nice homeomorphisms and continuous transformations. I wouldn't say it really helps with learning topology beyond imparting the idea that you only care about shapes up to homeomorphism, i.e. if one shape can be continuously changed into the other and the other can be continuous changed back, then they are the same. When properly learning basic topology, it is a lot of manipulating sets and functions rather than looking at shapes. Understanding the shapes and spaces you are working with is important, as you are able to intuitively guess at the properties of those spaces without having to do actual computations, however if you want to prove things, you actually do have to do computations.
@@mujtabaalam5907 Indeed, they are not homeomorphic. The fundamental group of a sphere is trivial and the fundamental group of a torus is Z * Z. This is because the polar coordinate transformation is not a homeomorphism but rather just a continuous map. It is a homeomorphism from (0,2pi] x (0, infty) to R^2-{0}.
Yaaaaas! I'm truly in love and the only question I have is: should I show this to all my G9 students or save it only for the Math Club members? Hahahaha
@@xicufwm Totally show it to them! I’m not into math at all but this game is really peaking my interest, plus it can make things easier to understand for people who learn best with physical/interactive objects
Nobody: I really liked the visual asthetics of the "how to turn a sphere inside out" classic youtube video, I wish there was a video game about it The Devs: TANDEEZE NUTS
It's really interesting to see a puzzle game like this and it feels somewhat similar to pottery as you need to figure out the side curves while using a wheel. Hope to see more content!
"I wonder how the algorithm for close enough works?" I expect that it's using a parameter space where each coefficient is for x-stretch, y-stretch, amount of sine-wave, amount of curvature around a cylinder, etc. So we would get a list of numbers that describes exactly the transformations that the surface has undergone. We can define distance in this parameter space via the euclidean metric (sqrt(a^2 + b^2 + c^2 ...)). Then there's just a threshold *parameter* distance that counts as success.
I don't know if that would work for different solutions, and there definitely are multiple sets of transformations which produce the same result. Or maybe it would? I guess it's probably all matrices so on second thought yeah, it's probably a metric on the matrix representation.
I think it's more of a mesh volume comparison. It tries a bunch of relative positions, and scores them based on how "close" a kind of voxel building the mesh are to the target.
Tyler’s really like : “ah yes I see the checkers alight to form this demented geometry which I may manipulate based on the X and y axis and move between dimensions” Then also have his : “:0 whAt AboUT tHiS APpLe?” moments
Like another guy said, this game has felt pretty easy to me so far, likely due to my use of 3D modeling software. The only parts that have been strange to me are the wavy line thing, as that is not generally a feature of 3D modeling programs. The stretched one is, well, stretching, and the circle one is the revolve tool. To me it was pretty intuitive in most of the ones using a circle what you needed to put in to get the object, same with turning it diagonally once you got the squiggly shape. The only parts that have been confusing me are the squiggles themself, very hard for me to visualize what it's going to look like.
9:55 I think the best way to think about how the graph tranforming to the polar graph (the circle one) is that it extrudes the shape around the center axis in a circle, or connecting the left and right part of the shape by bending it like a cylinder
@@anteshell I'm not saying it IS extruding, I'm trying to give explain it a different way for people who are having a hard time understanding whats happening, since this is a lot different from the usual grid-type content Tyler plays
13:40 The long/short transformation makes it possible to scale any 3D object down, you just have to get the right rotations, so you only needed to shrink it in height.
This is so cool, I'd absolutely love to see more of it, I really love weird topology fuckery and this game seems like the perfect mix between mind bending maths and cool puzzles
This is the coolest puzzle game I have ever seen! As someone who loves both puzzles and math my brain is getting really excited see familiar shapes and concepts that I learned in my calc 3 class in college. For someone who never took anything more than algebra this game would be an excellent mind binding puzzle on it’s own, but for someone who knows a bit of calculus this can be an excellent tool for visualizing integrals and other mathematical concepts in three dimensions!
This is one of the most interesting games I've seen in awhile (my own opinion, of course). I could see myself playing this for hours just to see what I could make.
Incredibly cool concept, frankly this should be required playing for students coming into multivariable calculus Also how the absolute heck is this not jank as all heck??
The keyword here is polar coordinates. It always amazes me how quickly Taylor grasps mathematical concepts and understands them on intuitive level. I don't know what's his education, but he'd make a good mathematician.
I guess the solution checker works by tracking the order of transformations and rotations and that the offset on the boards is within acceptable limits.
11:24 i'd imagine the main part is just which transformations were applied in what orentiations, which has to be perfect (normalized with respect to symmetries and "undoing" transformations), and it's more forgiving for the exact placement of the sheet on the grid in each transformation, maybe just like within +- 1 unit
If I had to guess as to how the forgiveness factor worked, I'd wager that each available transform is just a matrix (linear algebra). Where you place the shape on these transforms adjusts the values used by the transform. Finally, it sees if each component of your matrix is close enough to the solution. Matrix transformations are dependent on the order you do them.
while i know very little about how to program a game beyond the most bare basics imaginable, perhaps the "close enough" measuring of the shape has to do with either a value range of the object's properties or the formed function to create the shape? like, if we pretend an axis is a sine function or something, it would compare the target range to the submitted one or something within a reasonable percentage.
Daaaaaamn, a geometry puzzle game with actual transformations?! Is it Christmas already? :D PLEASE continue this series!!! By the way, the one from the grid to the circle is called a "polar transformation". :)
8:01 could literally rotate and stretch btw with your explanation i finally understand what it does like- i thought it just teleported the exact column in the other column there but i guess it just rotates your shape around a center huh
An alternate way to think about the circle transformation is that each horizontal row on the checkerboard becomes a ring on the circle board. This explains why horizontal objects get wrapped around to make a circular shape.
This is really cool. I feel like the presentation could be improved and make it more like a game than a series of puzzles, but the base functionality of transforming everything in real time is crazy in itself.
The explanation of how the transformations work with Tyler's face were 11/10, ben you're an icon
Besides the circle.
I think it should've been wiggly for the wiggle checker
But bro never had a clue when he tested them, it was obvious when it would work and when it wouldn’t
Oops
〰️〰️〰️
I love topology and a game that allows people to work on spacial visualization and topology, and teaches how to take a slice of an object and reverse engineer a design AND can teach coordinate manipulation like from rectangular to polar form is SICK, please more of this
So far, we only saw linear, trigonometric and polar transformations, so it's not quite topology - that would be more about matching hole numbers. ;)
Is this what you want 12:10 ?
Perchance, do you know the difference between a coffee mug and a donut?
I’m trying to understand how they coded the correct solutions, it seems simple from an outside point but that looks like hell to code.
@@ASaltyAcc that's really easy actually: each transformation is a matrix, multiple transformations is just a matrix multiplication. The desired shape (i.e. an equation with three variables) has a "solution matrix" attached and you compare the two (solution vs. user created). For the general shape you check if certain values are zero, positive or negative and then you just state an error for each of the fields that a user is allowed to be off. 🤷
Rotating or moving the user shape changes the transformation matrix as well of course. I find it more fascinating that we're at a processing power that allows this to be calculated on the fly 😉
I love that all the circular transformations were basically a visual representation of disc/washer method for volume calculations in calculus
Exactly what I was thinking
God i hated that unit
Yeah this is basically exactly how I visualized volume in calculus
@@kaibow7209your pfp is the same as the one I used to have lol. RIP lil bub
I was just visualizing what profile i wpuld revolve to get that shape in solidworks
I guess the CAD classes I took were worth it because this game seems pretty easy to me so far - not that that makes it any less fun, I absolutely love this one
Man, and Tyler looks like he's just struggling through it. I am in awe of youa abilities
It's cool to see that his outstanding puzzle solving ability powers through fairly quickly despite not having trained his brain specifically in 3D CAD-type stuff. Learning is cool
Yeah same, the revolve tool in Blender helped the circle thing feel very intuitive. And the stretched one is pretty obvious for similar reasons.
Agreed. I was yelling at my screen the entire time Tyler was on that cake looking level
@@-NGC-6302- Cause it's nowhere near as complex as you are desperately trying to make it. Kinda seems like you just wanted to tell everyone you took CAD courses.
When he tries to explain a curve he's looking for, he brings out the post it note and bends it the exact same as the last time he was trying to explain a curve, leaving me more confused
3D Topography is crazy
That's the trick
It's the same shape each time
The perfect curve
because, get this: It was the same curve!
Is that tube??
UA-cam.
After looking it up I've noticed that this is actually a sequel to another game called "Engare", and based on this I think it might be interesting to check out.
This game is really stirring up the mathy part of my brain. It's super cool! This game might even be a good thing to use when teaching math stuff
I can't tell if topologists would love or hate this game
@@Phriedah It shows some nice homeomorphisms and continuous transformations. I wouldn't say it really helps with learning topology beyond imparting the idea that you only care about shapes up to homeomorphism, i.e. if one shape can be continuously changed into the other and the other can be continuous changed back, then they are the same. When properly learning basic topology, it is a lot of manipulating sets and functions rather than looking at shapes. Understanding the shapes and spaces you are working with is important, as you are able to intuitively guess at the properties of those spaces without having to do actual computations, however if you want to prove things, you actually do have to do computations.
@@ethanbottomley-mason8447 But in this game you can change a sheet into a torus or a sphere. I don't think those are homeomorphic, are they?
@@mujtabaalam5907 Indeed, they are not homeomorphic. The fundamental group of a sphere is trivial and the fundamental group of a torus is Z * Z. This is because the polar coordinate transformation is not a homeomorphism but rather just a continuous map. It is a homeomorphism from (0,2pi] x (0, infty) to R^2-{0}.
This feels like it'd be very useful for teaching advance geometry in a class.
Yaaaaas! I'm truly in love and the only question I have is: should I show this to all my G9 students or save it only for the Math Club members? Hahahaha
@@xicufwm the plebs dont deserve to see this, save it for the club
@@xicufwmI disagree, show it in the regular class. Maybe it'll spark an interest or two among students who dislike / are not confident in maths.
@@xicufwm Totally show it to them! I’m not into math at all but this game is really peaking my interest, plus it can make things easier to understand for people who learn best with physical/interactive objects
Nobody: I really liked the visual asthetics of the "how to turn a sphere inside out" classic youtube video, I wish there was a video game about it
The Devs: TANDEEZE NUTS
I just randomly got that one in my recommended a few days ago-
It was a good video tbh
@@crazybeatrice4555 *_R E M E M B E R, Y O U M U S N ' T T E A R I T O R C R E A S E I T_*
@@JustAnotherCommenter "This is not what a brother and sister are supposed to do!"
incest??
It's really interesting to see a puzzle game like this and it feels somewhat similar to pottery as you need to figure out the side curves while using a wheel. Hope to see more content!
"I wonder how the algorithm for close enough works?"
I expect that it's using a parameter space where each coefficient is for x-stretch, y-stretch, amount of sine-wave, amount of curvature around a cylinder, etc. So we would get a list of numbers that describes exactly the transformations that the surface has undergone. We can define distance in this parameter space via the euclidean metric (sqrt(a^2 + b^2 + c^2 ...)). Then there's just a threshold *parameter* distance that counts as success.
I don't know if that would work for different solutions, and there definitely are multiple sets of transformations which produce the same result. Or maybe it would? I guess it's probably all matrices so on second thought yeah, it's probably a metric on the matrix representation.
I suspect that the transformations don’t quite commute, so a simple parameter space wouldn’t really be possible. Can’t prove it though.
I think it's more of a mesh volume comparison. It tries a bunch of relative positions, and scores them based on how "close" a kind of voxel building the mesh are to the target.
Pretty sure it's a mesh approach since to have commute property you'd need a mirror operation?
Stop my brain is already melting
It's crazy how the checkerboard patterns stay the same, so every single shape is possible from the start
Tyler’s really like : “ah yes I see the checkers alight to form this demented geometry which I may manipulate based on the X and y axis and move between dimensions”
Then also have his : “:0 whAt AboUT tHiS APpLe?” moments
The coding of this mustve been a nightmare
Props to whoever made this game
This game implicitly teaches you different coordinate systems and transformations. Actually used a lot in physics.
14:08 I'll let you know that I want to see more of this. I like this game.
Like another guy said, this game has felt pretty easy to me so far, likely due to my use of 3D modeling software. The only parts that have been strange to me are the wavy line thing, as that is not generally a feature of 3D modeling programs. The stretched one is, well, stretching, and the circle one is the revolve tool. To me it was pretty intuitive in most of the ones using a circle what you needed to put in to get the object, same with turning it diagonally once you got the squiggly shape. The only parts that have been confusing me are the squiggles themself, very hard for me to visualize what it's going to look like.
This matching design kind of game feels like an expansion on an old flash game called Factory Balls. I love it!
9:55 I think the best way to think about how the graph tranforming to the polar graph (the circle one) is that it extrudes the shape around the center axis in a circle, or connecting the left and right part of the shape by bending it like a cylinder
@@anteshell I'm not saying it IS extruding, I'm trying to give explain it a different way for people who are having a hard time understanding whats happening, since this is a lot different from the usual grid-type content Tyler plays
@@anteshell Not here to argue bro I'm here to help clueless people 😂
@@anteshell 😂
@@anteshell isnt that very semantic and not necessary to just understand what’s going on
@@anteshell get off your damn high horse. as it was used in these levels, it has identical results and a similar thought process to an extrusion
I love your content, Tyler, and I ant wait to see more of this game on your channel!
So far I'm loving this game.
Would love to see you make more videos of it
I love the names and explanations he comes up with for the Torus and Wormhole.
Loved watching this game, holy moly.
I want so much more content on this game
The editing and the silly comments were spot-on with this one
Fun fact: the first shape is the Arabic letter ع
and the Urdu letter: ع which is similar to غ
11:55 "demented geometry" is the perfect way to describe what's going on! As a Math teacher, I love it! Please show us the rest of this game!
Amazing. Please more of this game. Edits are marvelous as well
This is one of the most interesting games I've seen. I want more
This game looks *awesome*, I hope you come back to it!!!
This is an incredibly compelling and clever game. I'm all about seeing more of this.
13:40 The long/short transformation makes it possible to scale any 3D object down, you just have to get the right rotations, so you only needed to shrink it in height.
12:18 🤣🤣😂 this is mind blowing. Would love to see more.
"I was just trying to make a wedding cake and I got transported to hell." sums this game up in 1 Sentence.
That is not a word, a sentence
PFF I didn't notice this until you pointed it out, thank you. XD@@slametdinatadinata645
This is so cool, I'd absolutely love to see more of it, I really love weird topology fuckery and this game seems like the perfect mix between mind bending maths and cool puzzles
As someone who likes math this video both entertained me and infuriated me. Thank you Tyler.
Love how complex the puzzles get with such simple mechanics. With a level editor this could go to crazy levels from how much you can do with this
a couple of puzzles looked like they could be solved in multiple ways with a different transformation order, which was pretty cool!
This is the coolest puzzle game I have ever seen! As someone who loves both puzzles and math my brain is getting really excited see familiar shapes and concepts that I learned in my calc 3 class in college. For someone who never took anything more than algebra this game would be an excellent mind binding puzzle on it’s own, but for someone who knows a bit of calculus this can be an excellent tool for visualizing integrals and other mathematical concepts in three dimensions!
The editing on this was amazing!!! Props to the editors as always!
“I was just trying to make a wedding cake and I got transported to hell.” Tyler, 2023
Obviously Ben's sense of style is impeccable
This is sick. Love this game and your commentary. Would love to see more videos.
I have a kitten named Wiggles. He is definitely wiggly. This game is very cool, Tyler. I also have a cat named Squiggles
That game sure does look addictive!! Can't wait to see more shapes!
I found your channel a couple years ago and youve entirely transformed my taste in games since then. Thank you so much
Enjoyed watching this a lot! Would love to see more videos of you playing Tandis!
This is one of the most interesting games I've seen in awhile (my own opinion, of course). I could see myself playing this for hours just to see what I could make.
Incredibly cool concept, frankly this should be required playing for students coming into multivariable calculus
Also how the absolute heck is this not jank as all heck??
they worked hard to make it lenient for sure
Wedding cakes are so expensive these days, requiring you to *travel to the depths of hell*
Keep making shapes. I am for topology!
I’m seeing shapes in this game that I never could’ve possibly imagined
wow this game is sick, simple but very deep
The keyword here is polar coordinates. It always amazes me how quickly Taylor grasps mathematical concepts and understands them on intuitive level. I don't know what's his education, but he'd make a good mathematician.
I love it when simple concepts can get this kind of mileage
this is an incredibly creative puzzle game, i love it already
12:20
"You ended up in the twelfth plane of torment while trying to make a... wedding cake?"
"I am not a clever man."
I guess the solution checker works by tracking the order of transformations and rotations and that the offset on the boards is within acceptable limits.
just from the intro i can tell this is gonna be a fun game
This was glorious! Would love to see more.
I forgot this game existed, but I'm so glad to see you play it!
And somehow you were able to nicely articulate the 3D shape you desired.
watching the very first section and learning this game has zero limits makes me happy
this is literally so satisfying i must get this
i don't think i've ever had a puzzle game provoke such a visceral "WOW" part of my brain before. please, more of this.
holy this game is training my restraint to backseat. i keep yelling at the screan but i also love seeing tyler find solutions i didnt think of.
loved the video. You explained it super well
11:24 i'd imagine the main part is just which transformations were applied in what orentiations, which has to be perfect (normalized with respect to symmetries and "undoing" transformations), and it's more forgiving for the exact placement of the sheet on the grid in each transformation, maybe just like within +- 1 unit
This seems like an amazing concept with a lot of potential
please make this into a series
broo im so excited to play this
If I had to guess as to how the forgiveness factor worked, I'd wager that each available transform is just a matrix (linear algebra). Where you place the shape on these transforms adjusts the values used by the transform. Finally, it sees if each component of your matrix is close enough to the solution. Matrix transformations are dependent on the order you do them.
This game seems very promising! Hope to see more of it on the channel soon.
I always found graph transformations satisfying. This game looks like so much fun!
Love the editors work
while i know very little about how to program a game beyond the most bare basics imaginable, perhaps the "close enough" measuring of the shape has to do with either a value range of the object's properties or the formed function to create the shape? like, if we pretend an axis is a sine function or something, it would compare the target range to the submitted one or something within a reasonable percentage.
Dude this looks so trippy
This feels like something you would see a star trek character playing in their off time
You have an amazing spatial imagination.
I'd have hit a wall as soon as the puzzle became a bit more complex than: "stretch this square".
really like the explanations on this one
would defintely watch more
THIS GAME IS SO SICK WHAT
this was extremely satisfying
Daaaaaamn, a geometry puzzle game with actual transformations?! Is it Christmas already? :D PLEASE continue this series!!!
By the way, the one from the grid to the circle is called a "polar transformation". :)
“A sphere and a donut are closely related” topologists: *screaming* HES GONE MAD!!!!
Well if you shrink the hole in a torus enough it becomes a double covering of a sphere but not exactly a sphere itself
I love Tyler's technical explanations here
MOAR MOAR MOAR MOAR
This game should be mandatory in every calculus class
8:01 could literally rotate and stretch
btw with your explanation i finally understand what it does like- i thought it just teleported the exact column in the other column there but i guess it just rotates your shape around a center huh
"I was just trying to make a wedding cake and got transported to Hell." Awesomely worded. :)
I did not expect to see Arabic letters on Aliensrock's channel today but hey I ain't complainin
Well this game will yelp with my non Euclidean geometry course, i think
That moment when you make a circle more circular and reality fractures
An alternate way to think about the circle transformation is that each horizontal row on the checkerboard becomes a ring on the circle board. This explains why horizontal objects get wrapped around to make a circular shape.
good game please more
This is really cool. I feel like the presentation could be improved and make it more like a game than a series of puzzles, but the base functionality of transforming everything in real time is crazy in itself.
This looks sick, I'd love to see more 🤗
Also, as always, editing is perfect. 👌
This game is amazing!
This is really entertaining! I would like more please :)
This game feels like it needs a % bar to drive perfectionist crazy
What a cool concept! I really love anamorphic transformations
This game reminds me so much of multivariable calculus, in a good way