Okay just saw a post where someone was talking about the correct order to do maths in an equation acronym and they said 'PEMDAS'??? I learned BEDMAS wtf is this shit
so
These are the only ones I've heard but idk there may be more
Hey so you remember this thing that everyone on mathblr got excited about recently?
This is the hat, and it's what's called an "aperiodic monotile". This means that no matter how you arrange copies of this tile, you can never get an arrangement that will repeat infinitely (think of it like the irrational numbers of tilings). This was big news in mathematics as while sets of more than one tiles have been found that are aperiodic (e.g: The Penrose Tiles), this was the first tile that's aperiodic by itself, hence "monotile". (There are some caveats to this but that's not important for understanding this post)
However.
If you look at images of the hat tiling, you may notice something.
If you look at the tiles labled 1 and 2, you'll see that one's a reflected copy of the other. In fact, any infinite arrangement with hats requires you to you mix unreflected and reflected tiles. Which raises the question: is it possible to have an aperiodic monotile that doesn't need reflections?
Presenting the Spectre, A chiral aperiodic monotile.
Using only translation and rotation, any arrangement of copies of this tile will never repeat.
Mathematically speaking, this is really fucking cool.
The paper on it is still in preprint, but hopefully I won't need to retract this post. A copy of it can be found here and a post going into some more details of how the shape was discovered is here.
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For those with different grade/level structures, in the US 10th grade is typically age 15–16, 11th grade age 16–17, and 12th grade age 17–18.
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