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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 volume measurement was developed to estimate what volume of a round log would be usable timber after processing, in effect attempting to ‘square’ the log and allow for waste. The hoppus ton (HT) was also a traditionally used unit of volume in British forestry. One hoppus ton is equal to 50 hoppus feet or 1.8027 cubic meters.
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
Floor Area ratio is sometimes called floor space ratio (FSR), floor space index (FSI), site ratio or plot ratio. The difference between FAR and FSI is that the first is a ratio, while the latter is an index. Index numbers are values expressed as a percentage of a single base figure. Thus an FAR of 1.5 is translated as an FSI of 150%.
If a square tiling is shifted by the width of a tile, parallel to the sides of the tile, the result is the same pattern of tiles as before the shift. A shift (formally, a translation) that preserves the tiling in this way is called a period of the tiling. A tiling is called periodic when it has periods that shift the tiling in two different ...
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