Talk:Circle Limit III

A fact from Circle Limit III appeared on Wikipedia's Main Page in the Did you know column on 5 July 2013 (check views). The text of the entry was as follows:

Did you know... that M. C. Escher's woodcut Circle Limit III was inspired by an illustration of a hyperbolic tessellation (example pictured) in a paper by H. S. M. Coxeter?

A record of the entry may be seen at Wikipedia:Recent additions/2013/July. The nomination discussion and review may be seen at Template:Did you know nominations/Circle Limit III.

Wikipedia

Visual arts

This article is within the scope of WikiProject Visual arts, a collaborative effort to improve the coverage of visual arts on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.Visual artsWikipedia:WikiProject Visual artsTemplate:WikiProject Visual artsvisual arts

Mathematics Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Low	This article has been rated as Low-priority on the project's priority scale.

Symmetry comparison

I made a quick attempt to overlay a Tritetragonal_tiling from KaliedoTile with curved edges. It could be done more exactly, but also depends on whether original image is a photo and what perspective distortions existed there. Tom Ruen (talk) 23:27, 5 July 2013 (UTC)[reply]

I replaced with a more careful adjustment and looks better. So Escher's white line as based on the tiling lines (which are not straight), and also the white area giving the line width is mostly borrowed from the larger square areas. Tom Ruen (talk) 03:27, 6 July 2013 (UTC)[reply]

File:Circle_limits_III_with_overlay.png

We don't know exactly what Escher did, and woodcuts are not exactly a medium that leads to great geometric accuracy. But bending the curves into the squares is exactly what one would expect when replacing hyperbolic line segments by hypercycles, so your overlay is consistent with that. It might make sense to include the image itself in the article (as a replacement for the existing tritetragonal image, not in addition to it — I think we should make an effort to keep the images that are not of the artwork in question few in number) but without including much text analyzing the overlap, because that would probably be WP:OR. —David Eppstein (talk) 04:56, 6 July 2013 (UTC)[reply]

I agree on OR, hence on talk here! And in agreement on why here's a comparison of the tiling centered on a triangle. You can see the projective lines "wiggle" making concave triangle edges, so Escher's artistic adjustment effectively smoothed out these wiggles of the projective view. Tom Ruen (talk) 05:06, 6 July 2013 (UTC)[reply]