Talk:Circle Limit III

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)
 * 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)
 * 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)
 * Uniform_tiling_433-t0_3-fold.png
 * 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)