Breakthrough in mathematics! The einstein tile

[Oler-yxxj]

I love it when there is a breakthrough in a problem that was covered by Numberphile, it makes it feel so close.

[eryqeryq]

I like to think of aperiodic patterns as two-dimensional irrational numbers

[ComBlogger]

My left ear really appreciated the direct translation of Einstein to "One Stone" instead of the reference to Albert Einstein

[mizan]

My left ear is now officially more knowledgeable than my right one

[no-bkzx]

My left ear definitely enjoyed this video.

[theunknownunknowns]

Yeah, but when can I get them for my bathroom renovation? 😂

[taimunozhan]

Aperiodic patterns with the new einstein hat tile (or any of the infinite related ones) need to include a mirrored version of that tile. The question of whether an aperiodic tiling can be made using only one kind of tile without mirroring is still open.

[realDonaldMcElvy]

"It's called an einstein tile" - Albert Einstein

[thomaskaldahl]

Minor correction (I think)! A tiling (referring to the configuration) is NONperiodic if it never repeats. A tileset (referring to the constituent tiles) is Aperiodic if it is such that regardless of how you tile the plane, you can only do it nonperiodically.

There are some boring examples of tilings that never repeat. For example, fill the plane with a bunch of horizontal 2x1 rectangles, then choose some squares formed by pairs of lengthwise adjacent tiles and rotate them 90°. You can do this in a way that ensures the tiles never repeat.

What's fascinating is that the aperiodic monotile just cannot tile the plane periodically, no matter how hard one tries!

[Jabranalibabry]

That printing technician is the OG, he just needed to retire so he could math

[elmojackson]

In german, "Einstein" means "a stone", so it is a perfect name.

[harishsundararaman]

Perfect. Now to make a board game from it

[-___-g]

Please don’t stop posting videos. I love the way you do things:)

[gornser]

"Ein Stein" is German for "one stone". Pretty, too

[dankmemes]

my left ear is now smarter than my right ear thank you

[nahommerk]

I am pretty sure this is something Vsauce will go on a quest to find in the middle of the night for no reason at all...😂

[samuelgunter]

my left ear loved this video, but my right ear just thought if was one of those infinite number of muted videos

[trucid]

Now to find one with the fewest edges, or to prove that the one that was found is optimal.

[flyingbicycles]

This would be like if P=NP. If just one NP problem can be solved in P, every NP problem can be solved in P.

[gabedarrett]

That's pretty neat! I wonder what applications we'll eventually discover...