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

〰️〰️〰️

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 😉

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

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

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??

KZfaq.

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??

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

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}.

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

@@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

That is not a word, a sentence

PFF I didn't notice this until you pointed it out, thank you. XD@@slametdinatadinata645

they worked hard to make it lenient for sure

MOAR MOAR MOAR MOAR

And yet he still forgets about the 3rd dimension