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The first tile cutter was designed to facilitate the work and solve the problems that masons had when cutting a mosaic of encaustic tiles (a type of decorative tile with pigment, highly used in 1950s, due to the high strength needed because of the high hardness and thickness of these tiles).
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.
B-tiles can be related to such A-tiles in two ways: If B S has the same size as A L then B L is an enlarged version φ A S of A S, with side lengths (φ, φ, φ 2 = 1 + φ) – this decomposes into an A L tile and A S tile joined along a common side of length 1.
For floors, quarry tile is usually set in a thick bed of cementitious mortar. For wall applications, it can be set in either a thick bed of cementitious mortar or a thin bed of mastic. For both floors and walls, the joints between tiles are usually grouted with cementitious grout. Grout joints are traditionally about 3 ⁄ 8 inch in width.
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