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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.
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 ...
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.
A filled square with a side length of a I x = a 4 12 I y = a 4 12 {\displaystyle {\begin{aligned}I_{x}&={\frac {a^{4}}{12}}\\[3pt]I_{y}&={\frac {a^{4}}{12}}\end{aligned}}} [ 6 ] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through ...
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%.
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Hong Kong law Chapter 123F, Building (Planning) Regulations, Regulation 23 sect 3 sub-paragraph (a) defined that: Subject to sub-paragraph (b), for the purposes of regulations 19, 20, 21 and 22, the gross floor area of a building shall be the area contained within the external walls of the building measured at each floor level (including any floor below the level of the ground), together with ...
Any tiling by these tiles can only exhibit a hierarchy of square lattices: the centre of any orange square is also a corner of a larger orange square, ad infinitum. Any translation must be smaller than some size of square, and so cannot leave any such tiling invariant. A portion of tiling by the Robinson tiles
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