Binary tiling: Difference between revisions

Revision as of 18:48, 27 October 2024

Revision as of 18:52, 27 October 2024

Line 3:

{{Use list-defined references|date=September 2024}}

{{CS1 config|mode=cs1}}

[[File:Hyperbolic binary tiling.png|upright=1.2|alt=Binary tiling on Poincare disk|thumb|A binary tiling displayed in the [[Poincaré disk model]] of the [[hyperbolic plane]]. Each sidetile of a tileedge lies on a [[horocycle]] (shown as circles interior to the modeldisk) or a hyperbolic line (shown as arcs of circles perpendicular to the modeldisk boundary). TheseThe horocycles and lines are all asymptotic to a commonan [[ideal point]] located at the right side of the Poincaré disk.]]

In [[geometry]], a '''binary tiling''' (sometimes called a '''Böröczky tiling'''){{r|df}} is a [[tiling of the hyperbolic plane]], resembling a [[quadtree]] over the [[Poincaré half-plane model]] of the hyperbolic plane. The tiles are congruent, each adjoining five others. They may be convex [[pentagon]]s, or non-convex shapes with four sides, alternatingly line segments and [[horocycle|horocyclic]] arcs, meeting at four right angles.