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Girih Tilings
''Girih'' tiles are a set of five tiles that were used in the creation of Islamic geometric patterns using strapwork (''girih'') for decoration of buildings in Islamic architecture. They have been used since about the year 1200 and their arrangements found significant improvement starting with the Darb-i Imam shrine in Isfahan in Iran built in 1453. Five tiles The five shapes of the tiles are: * a regular decagon with ten interior angles of 144°; * an elongated (irregular convex) hexagon with interior angles of 72°, 144°, 144°, 72°, 144°, 144°; * a bow tie (non-convex hexagon) with interior angles of 72°, 72°, 216°, 72°, 72°, 216°; * a rhombus with interior angles of 72°, 108°, 72°, 108°; and * a regular pentagon with five interior angles of 108°. These modules have their own specific Persian names: The quadrilateral tile is called Torange, the pentagonal tile is called Pange, the concave octagonal tile is called Shesh Band, the bow tie tile is called Sormeh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Girih Tiles
''Girih'' tiles are a set of five tiles that were used in the creation of Islamic geometric patterns using strapwork (''girih'') for decoration of buildings in Islamic architecture. They have been used since about the year 1200 and their arrangements found significant improvement starting with the Darb-i Imam shrine in Isfahan in Iran built in 1453. Five tiles The five shapes of the tiles are: * a regular decagon with ten interior angles of 144°; * an elongated (irregular convex) hexagon with interior angles of 72°, 144°, 144°, 72°, 144°, 144°; * a bow tie (non-convex hexagon) with interior angles of 72°, 72°, 216°, 72°, 72°, 216°; * a rhombus with interior angles of 72°, 108°, 72°, 108°; and * a regular pentagon with five interior angles of 108°. These modules have their own specific Persian language, Persian names: The quadrilateral tile is called Torange, the pentagonal tile is called Pange, the concave octagonal tile is called Shesh Band, the bow tie tile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'', also widely referred to as ''Science Magazine'', is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose Tiling
A Penrose tiling is an example of an aperiodic tiling. Here, a ''tiling'' is a covering of the plane by non-overlapping polygons or other shapes, and ''aperiodic'' means that shifting any tiling with these shapes by any finite distance, without rotation, cannot produce the same tiling. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s. There are several different variations of Penrose tilings with different tile shapes. The original form of Penrose tiling used tiles of four different shapes, but this was later reduced to only two shapes: either two different rhombi, or two different quadrilaterals called kites and darts. The Penrose tilings are obtained by constraining the ways in which these shapes are allowed to fit together in a way that avoids periodic tiling. This may be done in s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasicrystalline
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold. Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling,Alan L. Mackay, "Crystallogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similar
__NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. A time developing phenomenon is said to exhibit self-similarity if the numerical v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Steinhardt
Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences. Steinhardt is best known for his development of new theories of the origin, evolution and future of the universe. He is also well known for his exploration of a new form of matter, known as quasicrystals, which were thought to exist only as man-made materials until he co-discovered the first known natural quasicrystal in a museum sample. He subsequently led a separate team that followed up that discovery with several more examples of natural quasicrystals recovered from the wilds of the Kamchatka Peninsula in far eastern Russia. Several years later, he and collaborators reported the accidental synthesis of a previously unknown type of quasicrystal in the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Lu
Peter James Lu, PhD (陸述義) is a post-doctoral research fellow in the Department of Physics and the School of Engineering and Applied Sciences at Harvard University in Cambridge, Massachusetts. He has been recognized for his discoveries of quasicrystal patterns (girih tiles) in medieval Islamic architecture, early precision compound machines in ancient China, and man's first use of diamond in neolithic China. Early life and education Lu was born in Cleveland, Ohio and grew up in the Philadelphia suburb of West Chester, Pennsylvania. His early childhood interest in rockhounding led to his winning national gold medals in the "Rocks, Minerals, and Fossils" event at four National Science Olympiad tournaments. Lu graduated from B. Reed Henderson high school in West Chester in 1996. Lu matriculated at Princeton University in September, 1996, and was advised in his first year by geology professor Kenneth S. Deffeyes. He studied organic chemistry with Maitland Jones, Jr., with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Girih
''Girih'' ( fa, گره, "knot", also written ''gereh'') are decorative Islamic geometric patterns used in architecture and handicraft objects, consisting of angled lines that form an interlaced strapwork pattern. ''Girih'' decoration is believed to have been inspired by Syrian Roman knotwork patterns from the second century. The earliest ''girih'' dates from around 1000 CE, and the artform flourished until the 15th century. ''Girih'' patterns can be created in a variety of ways, including the traditional straightedge and compass construction; the construction of a grid of polygons; and the use of a set of ''girih'' tiles with lines drawn on them: the lines form the pattern. Patterns may be elaborated by the use of two levels of design, as at the 1453 Darb-e Imam shrine. Square repeating units of known patterns can be copied as templates, and historic pattern books may have been intended for use in this way. The 15th century Topkapı Scroll explicitly shows girih patterns toge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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