Square tiling

A rectangular school hallway is to be tiled with 6-inch-square tiles. The hallway is 72 feet long and 10 feet wide. Lockers along both walls narrow the hallway by 1 foot on each side. How many tiles are needed to cover the hallway... 

The Problem Using your yardstick, you measure the length of a room to be 6 yards and its width to be 5 yards. You plan on putting in 1-foot-square tiles. How many tiles will you need ... 

The triangular and hexagonal tilings are dual to each other, while the square tiling is self-dual. For other parameters (r, q), the tiling r, q lives in hyperbolic space H2 (see many pictures in [EpsOO]) but we will not need it. 

For such uses the laminate normally is bonded to a fibreboard or chipboard substrate (typically, 6 mm thick), which is backed with a compensating laminate to prevent bowing, then cut into square tiles or planks that are tongued and grooved. 

How many six-inch square tiles are needed to tile the floor in a room that is 12 feet by 15 feet ... 

Use an open-field arena that has 8x8 square tiles. Hurst (1988, 1989) used an arena 1.2 x 1.2 m large with 15 x 15 cm tiles. (One commercially available arena has 7x7 tiles, but will work, too). We will divide the arena into four quadrants (these may not be of entirely equal size see above). We will run two tests. 

The square tiling model has some attractive features reminiscent of real glasses, such as cooperativity, a relaxation spectrum that can be fit by the KWW equation, and a non-Arrhenius temperature-dependence of the longest relaxation time (Fredrickson 1988). However, the existence of an underlying first-order phase transition in real glasses is doubtful, and the characteristic relaxation time of the tiling model fails to satisfy the Adam-Gibbs equation. 

Figure 4.25 A glassy configuration of the square tiling model on a periodic 50 x 50 square lattice generated by a Monte Carlo simulation. (From Fredrickson 1988, with permission.)...

Clearlight, also called window pane, has appeared in a carrier of small film pyramids (many colors). This form was achieved by spraying a mixture of jelling agent on to plastic light covers of small pyramids. Small film squares (tiles) appeared containing 210 )j,g. of LSD salt (1974),... 

The cubic bond-orientational order (BOO) model of Trebin and coworkers [45], [46] is an attempt to rectify these theoretical problems. Originally formulated for crystals, the central idea of BOO is that the positional order of the atoms can be lost (due to formation of defect pairs or fluctuations) while still retaining the orientational order of the bonds. An analogous situation would occur for a floor loosely tiled with square tiles. If the sides of the tiles are all aligned properly, but the tiles are not fitted together correctly, orientational order is retained while positional order is lost. 

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