How to make an einstein tile

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Reading up on it, the guy who discovered it, David Smith, found the patterns it made (or lack thereof) curious and told a computer scientist friend about it, Craig Kaplan.

It makes me wonder how many deep mathematical objects were serendipitously discovered by people just playing around, and how many never got announced because they had no idea how significant it was.

UltimateHairDryer
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Enthusiasm is almost always contagious. Thank you

louisdavis
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It's funny, when I first heard about this, my first though was that it could have been discovered by a non-mathematician. it's one of these artefacts which make intuitive sense and can (at least at first glance) be verified to work fairly easily. For example finding a counter-example to a conjecture by accident has a much higher probability to happen if it concerns concrete objects such as tillings, because there are many more people manipulating them than there are mathematicians actively trying to solve the problem in the abstract

ApprendreSansNecessite
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Thank you, Jade! I know a lot of people don't like shorts, but I find them good in delivering a small piece of new info, or as a sort of preview for a full length video. Hope you keep making them. :)

vsm
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Could you do a follow-up on why you need to group these kites together into the "Einstein tile"? That is, what prevents you from making an aperiodic tiling with just the underlying kite shapes?

tuures.
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We like everything you explain to us 🥰

ashwinrawat
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I would probably explain the construction process this way: subdivide an equilateral triangle, add reflections of some of the subdivisions, then finally add a reflection of one of the reflections.

On my feed I've seen a number of "beginner" Youtube channels discuss this, but yours is the first experienced channel to take it on. Thank you.

BTW, I made a little mathematical discovery of my own a month or two ago, not a breakthrough, not a solution to any problem, but just something that made the mathematicians I shared it with say "oooh, shiny".

apm
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Is it just me or is this girl just a wholesome mathematician lady❤

gracetonsanthmayor
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That would make for a strange jigsaw puzzle.

patrickmccurry
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I appreciate that you let us know how it's made because seriously I was thinking it must have taken a lot of research to create that shape.

surajpatel
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One of the top 3 reasons I started watching YouTube shorts lately. Ur contents are just insightful and mind-boggling. ❤️ Amazing!! Keep posting!

siddhantsancheti
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Ah, not having read any of the detail I was surprised to learn the construction of the tile is so simple!

Aside: It's "einstein" as in "one stone", and nothing to do with Albert Einstein, so I don't think it should be capitalised in this case.

AthAthanasius
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Your pair is absolutely a delight for the eyes !

officialcommentcheckerofth
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I wonder what real world applications might arise from this discovery. Interesting subject matter delivered by an enthusiastic and charming host. That's why I keep coming back.

Saanichian
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Presumably this means the kite shape is periodic, but when grouped together as an Einstein tile, becomes aperiodic?

richardchang
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What program did you use for cutting up the hexagon?

donutman
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I’m so glad I found your channel! (Found it through the Einsteins tiles video!!)

Pan_Highlighter
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Your voice is ideal as a conception Creator... friendly, knowledgable but not boring! Thanks... Never heard of the concept but glad I Have now.

SpudderR
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But doesn't this tiling require mirroring in order to work? I thought there weren't any shapes discovered yet that tile aperiodically without mirroring or being disjointed?

skydude
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I have no idea what you are talking about, , but you are fun to watch explaining things ❤️❤️❤️😍

pomelChakma