Pentagon Tiling Proof Solves Century-Old Math Problem

Re:Pentagon Tiling Proof Solves Century-Old Math Problem by GregBuchholz on Tuesday July 11, 2017 @05:07PM (#14748076)

When it came to the description of "einsteins" (a single tile aperiodic tessellation), I couldn't help but think of the images in the 3rd edition of The Scheme Programming Language:

http://www.scheme.com/tspl3/binding.html#./binding:h0

http://www.scheme.com/tspl3/examples.html#./examples:h0

...Are there holes in those "tilings", or are the tiles not all the same shape, or am I misunderstanding what non-periodic means in this context?

And what is the name for those types of "self-surrounding" tiles on the cover:

http://www.scheme.com/tspl3/canned/large-cover.png

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Re:Pentagon Tiling Proof Solves Century-Old Math Problem by markegli on Tuesday July 11, 2017 @05:37PM (#14748314)

The tiles in an aperiodic tiling must guarantee that the tiling is not periodic simply by their shape.

https://en.wikipedia.org/wiki/Aperiodic_tiling

All three of the Scheme examples can be tiled periodically even though they aren't tiled periodically in the examples. How to tile them periodically is left as an exercise to the reader, but it's not hard.

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Re:Pentagon Tiling Proof Solves Century-Old Math Problem by GregBuchholz on Tuesday July 11, 2017 @06:03PM (#14748475)

Got to love this quote from the "Einstein Problem" page on Wikipedia:

https://en.wikipedia.org/wiki/Einstein_problem

"Depending on the particular definitions of nonperiodicity and the specifications of what sets may qualify as tiles and what types of matching rules are permitted, the problem is either open or solved."

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Re:Pentagon Tiling Proof Solves Century-Old Math Problem by Infernal on Tuesday July 11, 2017 @07:24PM (#14748928)

There's definitely something Douglas Adams-esque about that phrasing.

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Re:Pentagon Tiling Proof Solves Century-Old Math Problem by dwringer on Tuesday July 11, 2017 @05:29PM (#14748250)

The spiral images have tiles that are reflected, not just rotated. You'd otherwise need a third dimension to do another rotation. I think that might be considered two different tiles by the rules laid out in the article.

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Re:Pentagon Tiling Proof Solves Century-Old Math Problem by shmolyneaux on Tuesday July 11, 2017 @08:30PM (#14749237)

The banner image in the article appears to include reflected tiles.

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