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Tiling The Plane
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zellige
''Zellij'' ( ar, الزليج, translit=zillīj; also spelled zillij or zellige) is a style of mosaic tilework made from individually hand-chiseled tile pieces. The pieces were typically of different colours and fitted together to form various patterns on the basis of tessellations, most notably elaborate Islamic geometric motifs such as radiating star patterns. This form of Islamic art is one of the main characteristics of architecture in the western Islamic world. It is found in the architecture of Morocco, the architecture of Algeria, early Islamic sites in Tunisia, and in the historic monuments of al-Andalus (in the Iberian Peninsula). From the 14th century onwards, ''zellij'' became a standard decorative element along lower walls, in fountains and pools, on minarets, and for the paving of floors. After the 15th century the traditional mosaic ''zellij'' fell out of fashion in most countries except for Morocco, where it continues to be produced today. ''Zellij'' is found in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patterns
A pattern is a regularity in the world, in human-made design, 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. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict reg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Honeycomb
A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic Beeswax, wax cells built by honey bees in their beehive, nests to contain their larvae and stores of honey and pollen. beekeeping, Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about of honey to secrete of wax, and so beekeepers may return the wax to the hive after harvesting the honey to improve honey outputs. The structure of the comb may be left basically intact when honey is extracted from it by uncapping and spinning in a centrifugal machine, more specifically a honey extractor. If the honeycomb is too worn out, the wax can be reused in a number of ways, including making sheets of comb Wax foundation, foundation with hexagonal pattern. Such foundation sheets allow the bees to build the comb with less effort, and the hexagonal pattern of worker-sized cell bases discourages the bees from building the larger Drone (bee), drone cells. Fre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Tiling
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a truncated triangular tiling). English mathematician John Conway called it a hextille. The internal angle of the hexagon is 120 degrees, so three hexagons at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the triangular tiling and the square tiling. Applications The hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that the hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter. The optimal three-dimensional structure for making honeycomb (or rather, soap bubbles) was investigated by Lord Kelvin, who believed that the Kelvin structure (or body-centered cubic lattice) is optimal. However, the less regular Weaire–Phel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patterns In Nature
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time. In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. In the 20th century, the British mathematician Alan Turing predicted mechanisms of morphogenesis which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quilting
Quilting is the term given to the process of joining a minimum of three layers of fabric together either through stitching manually using a needle and thread, or mechanically with a sewing machine or specialised longarm quilting system. An array of stitches is passed through all layers of the fabric to create a three dimensional padded surface. The three layers are typically referred to as the top fabric or quilt top, batting or insulating material and the backing. Quilting varies from a purely functional fabric joinery technique to highly elaborate, decorative three dimensional surface treatments. A wide variety of textile products are traditionally associated with quilting that includes bed coverings, soft home furnishings, garments and costumes, wall hangings, artistic objects and cultural artefacts. A wide range of effects can be employed by the quilter that contribute to the final surface quality and utility of the quilted material. The quilter controls these effect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' not on ''R'', in the plane containing both line ''R'' and point ''P'' there are at least two distinct lines through ''P'' that do not intersect ''R''. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane. A modern use of hyperbolic geometry is in the theory of special relativity, particularly the Minkowski model. When geometers first realised they were working with something other than the standard Euclidean geometry, they described their geomet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alhambra
The Alhambra (, ; ar, الْحَمْرَاء, Al-Ḥamrāʾ, , ) is a palace and fortress complex located in Granada, Andalusia, Spain. It is one of the most famous monuments of Islamic architecture and one of the best-preserved palaces of the historic Islamic world, in addition to containing notable examples of Spanish Renaissance architecture. The complex was begun in 1238 by Muhammad I Ibn al-Ahmar, the first Nasrid emir and founder of the Emirate of Granada, the last Muslim state of Al-Andalus. It was built on the Sabika hill, an outcrop of the Sierra Nevada which had been the site of earlier fortresses and of the 11th-century palace of Samuel ibn Naghrillah. Later Nasrid rulers continuously modified the site. The most significant construction campaigns, which gave the royal palaces much of their definitive character, took place in the 14th century during the reigns of Yusuf I and Muhammad V. After the conclusion of the Christian Reconquista in 1492, the site became th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Islamic Geometric Patterns
Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6- to 13-point patterns by the 13th century, and finally to include also 14- and 16-point stars in the sixteenth century. Geometric patterns occur in a variety of forms in Islamic a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moroccan Architecture
Moroccan architecture refers to the architecture characteristic of Morocco throughout its history and up to modern times. The country's diverse geography and long history, marked by successive waves of settlers through both migration and military conquest, are all reflected in its architecture. This architectural heritage ranges from ancient Roman and Berber (Amazigh) sites to 20th-century colonial and modern architecture. The most recognizably "Moroccan" architecture, however, is the traditional architecture that developed in the Islamic period (7th century and after) which dominates much of Morocco's documented history and its existing heritage. This "Islamic architecture" of Morocco was part of a wider cultural and artistic complex, often referred to as " Moorish" art, which characterized Morocco, al-Andalus (Muslim Spain and Portugal), and parts of Algeria and even Tunisia. It blended influences from Berber culture in North Africa, pre-Islamic Spain (Roman, Byzantine, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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