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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.
In this tiling, isometric copies of appear in infinitely many orientations because the small angle of , , is not a rational multiple of . Radin found a collection of five prototiles, each of which is a marking of T {\displaystyle T} , so that the matching rules on these tiles and their reflections enforce the pinwheel tiling. [ 1 ]
Truchet tiles are square tiles decorated with patterns so they do not have rotational symmetry; in 1704, Sébastien Truchet used a square tile split into two triangles of contrasting colours. These can tile the plane either periodically or randomly. [46] [47] An einstein tile is a single shape that forces aperiodic tiling. The first such tile ...
Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.
Hopscotch is a popular playground game in which players toss a small object, called a lagger, [1] [2] into numbered triangles or a pattern of rectangles outlined on the ground and then hop or jump through the spaces and retrieve the object. [3] It is a children's game that can be played with several players or alone. [4]
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