The title suggests Will Hunting is a real person.
Elusive ‘Einstein’ solves a longstanding math problem
11–20 of 31 posts
Re: Elusive ‘Einstein’ solves a longstanding math problem
#12https://youtu.be/48sCx-wBs34 veritasium explanation of the tiling problem is excellent
Re: Elusive ‘Einstein’ solves a longstanding math problem
#13Important to note that the solution uses reflection. It uses the tile and a mirrored version of it. In my book, this means it is rather using two tiles than one. So the journey is not over. The question if a nonperiodic tiling of the plane is possible with one (non-mirrored) tile is still open.
Seems a bit stingy to say you don't get to flip the tiles over, though I guess it makes sense if you are talking tiles with only one "nice" side.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#14Important to note that the solution uses reflection. It uses the tile and a mirrored version of it. In my book, this means it is rather using two tiles than one. So the journey is not over. The question if a nonperiodic tiling of the plane is possible with one (non-mirrored) tile is still open.
> In my book, this means it is rather using two tiles than one.
I expected to see more about this. Are a given 2D shape and its mirror image generally considered the same shape by... the people who study this stuff? That would surprise me. So much so that calling this an "aperiodic monotile" doesn't feel right.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#15Important to note that the solution uses reflection. It uses the tile and a mirrored version of it. In my book, this means it is rather using two tiles than one. So the journey is not over. The question if a nonperiodic tiling of the plane is possible with one (non-mirrored) tile is still open.
Seems a bit stingy to say you don't get to flip the tiles over, though I guess it makes sense if you are talking tiles with only one "nice" side.
Also if you’re talking about the platonic ideal of a plane. There is no “flip” transformation purely within the 2D plane.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#16Important to note that the solution uses reflection. It uses the tile and a mirrored version of it. In my book, this means it is rather using two tiles than one. So the journey is not over. The question if a nonperiodic tiling of the plane is possible with one (non-mirrored) tile is still open.
> In my book, this means it is rather using two tiles than one. I expected to see more about this. Are a given 2D shape and its mirror image generally considered the same shape by... the people who study this stuff? That would surprise me. So much so that calling this an "aperiodic monotile" doesn't feel right.
Yes, "same shape" in this context means "isometric". Rotations and reflections are considered differences in the way the shape is placed into the plane, not differences in the shape itself.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#17Important to note that the solution uses reflection. It uses the tile and a mirrored version of it. In my book, this means it is rather using two tiles than one. So the journey is not over. The question if a nonperiodic tiling of the plane is possible with one (non-mirrored) tile is still open.
Seems a bit stingy to say you don't get to flip the tiles over, though I guess it makes sense if you are talking tiles with only one "nice" side.
It depends on if you're a mathematician interested in rigid transformations or if you manufacture ceramics.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#18Annoying that the headline writer went for the cheap "Einstein" as reference to clever human, ignoring that the guy (his name is Smith) found an "ein stein" (German: "one shape") that tiles aperiodically.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#19Annoying that the headline writer went for the cheap "Einstein" as reference to clever human, ignoring that the guy (his name is Smith) found an "ein stein" (German: "one shape") that tiles aperiodically.
Sorry to ruin your pun idea, but Stein doesn't mean geometric shape. The most common meaning is simply stone, but it can also mean board game piece.
Words you might use for these shapes instead would be Form (meaning shape) or Kachel (meaning tile).
Source: native speaker.
Re: Elusive ‘Einstein’ solves a longstanding math problem
#20Earlier quoted context omitted.
Seems a bit stingy to say you don't get to flip the tiles over, though I guess it makes sense if you are talking tiles with only one "nice" side.
Also if you’re talking about the platonic ideal of a plane. There is no “flip” transformation purely within the 2D plane.
What do you mean? Flipping is same as reflection, one of the rigid transformations
> The rigid transformations include rotations, translations, reflections, or any sequence of these. [...] All rigid transformations are examples of affine transformations.