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A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
This image is a derivative work of the following images: File:Hopscotch1900F294.png licensed with PD-US . 2008-07-18T04:14:05Z ScotchHopper 241x473 (6790 Bytes) {{Information |Description={{en|1=Hopscotch court; P. 357: Fig 294.—A Typical American Court with Ten Subdivisions.}} |Source=''The Outdoor Handy Book: For the Playground, Field, and Forest''.
Subtle alternating colors may be used to create a distinctive floor pattern, or the materials used may be the same, causing the floor to look uniform from a distance. Laying a herringbone floor is very challenging, since the multitude of small rows must be made to line up smoothly, which can be difficult in a room which is not perfectly flat.
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"Hopscotch to oblivion", Barcelona, Spain; an example of dark humor. A hopscotch court drawn such that the area where the final step would be is instead a sheer drop such as a building or cliff, such that any participant would fall to their death upon completion, is a motif occasionally seen in fiction, sometimes as a device for black comedy.
A normal tiling is a tessellation for which every tile is topologically equivalent to a disk, the intersection of any two tiles is a connected set or the empty set, and all tiles are uniformly bounded. This means that a single circumscribing radius and a single inscribing radius can be used for all the tiles in the whole tiling; the condition ...
In 1981, Grünbaum, Miller, and Shephard, in their paper Uniform Tilings with Hollow Tiles, list 25 tilings using the first two expansions and 28 more when the third is added (making 53 using Coxeter et al.'s definition). When the fourth is added, they list an additional 23 uniform tilings and 10 families (8 depending on continuous parameters ...
Infinitely many different pentagons can form this pattern, belonging to two of the 15 families of convex pentagons that can tile the plane. Their tilings have varying symmetries; all are face-symmetric. One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings ...