Talk:Binary tiling: Difference between revisions

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== View in the Poincaré disk model? ==

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:::Ok, done. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 01:55, 29 January 2018 (UTC)

:::: Nice! It would still be informative to see the shape of a single tile drawn "centered" on a Poincaré disk model. Then it would be more clear that the bottom pair edges are the same length as the top one. [[User:Tomruen|Tom Ruen]] ([[User talk:Tomruen|talk]]) 01:58, 29 January 2018 (UTC)

:::::It's not a regular polygon, so I'm not sure what "centered" means here. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 04:26, 29 January 2018 (UTC)

::::: Ha, that's why I put in quotes! Call it a [[centroid]], or somethig close, as you like. [[User:Tomruen|Tom Ruen]] ([[User talk:Tomruen|talk]]) 05:59, 29 January 2018 (UTC)

:::::{{Reply_to|Tomruen}} Or perhaps displayed in the band model, centered on a line going through a bunch of tiles. The band model preserves area near a line, so that would show the fact that the "parent" tiles are the same size as the "child" tiles. (For reference here is what the [[Order-4 pentagonal tiling|{5,4}]] looks like in the band model: http://bulatov.org/math/1001/band/tiling_425_band_00.png although I was thinking our band model would go through the centers of the tiles.) [[User:TheKing44|TheKing44]] ([[User talk:TheKing44|talk]]) 17:52, 29 January 2018 (UTC)

== Relation to this Aperiodic Tiling ==

The binary tiling is related to the one in figure 3 of [http://comp.uark.edu/~strauss/papers/hyp.pdf this paper] about a strongly aperiodic tiling of the hyperbolic plane (in particular, it also uses rectangles in the half-plane model, and they have a picture of the Binary tiling in Figure 1). Should we talk about in the article somehow?

(Maybe we could move this article to [[Böröczky tilings]], and describe all such tilings (including higher dimensional versions).) [[User:TheKing44|TheKing44]] ([[User talk:TheKing44|talk]]) 17:50, 29 January 2018 (UTC)

== Symmetry group ==

Theorem 3.12 of https://www.math.uni-bielefeld.de/baake/frettloe/papers/hyp-art-final.pdf describes the symmetry group of this tiling. (Just though y'all would like to know.) [[User:TheKing44|TheKing44]] ([[User talk:TheKing44|talk]]) 20:50, 29 January 2018 (UTC)

{{Talk:Binary tiling/GA1}}