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Download as PDF; Printable version; ... Help. A number of geometric arrangements of dots (or similar units) have been given special names in mathematics, art and ...
Download as PDF; Printable version; In other projects ... Dot patterns (1 C, 13 P) E. Elementary shapes ... (geometry) List of solids derived from the sphere ...
However, these dots were not always arranged in a quincunx pattern. The Oxford English Dictionary dates the first appearances of the Latin word in English as 1545 and 1574 ("in the sense 'five-twelfths of a pound or as '"; i.e. 100 old pence). The first citation for a geometric meaning, as "a pattern used for planting trees", dates from 1606.
The nth pentagonal number p n is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of ...
Consider two patterns made of parallel and equidistant lines, e.g., vertical lines. The step of the first pattern is p, the step of the second is p + δp, with 0 < δp < p. If the lines of the patterns are superimposed at the left of the figure, the shift between the lines increases when going to the right.
A form is an artist's way of using elements of art, principles of design, and media. Form, as an element of art, is three-dimensional and encloses space. Like a shape, a form has length and width, but it also has depth. Forms are either geometric or free-form, and can be symmetrical or asymmetrical.
A pattern is a regularity in the world, in human-made design, [1] or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns.
The union of all edges of a Cairo tiling is the same as the union of two tilings of the plane by hexagons.Each hexagon of one tiling surrounds two vertices of the other tiling, and is divided by the hexagons of the other tiling into four of the pentagons in the Cairo tiling. [4]