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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, and their Persian names, are: All sides of these figures have the same length, and all their angles are multiples of 36° (π/5 radians). All of them except the pentagon have bilateral (reflection) symmetry through two perpendicular lines. Some have additional symmetries. Specifically, the decagon has tenfold rotational symmetry (rotation by 36°); and the pentagon has fivefold rotational symmetry (rotation by 72°). The emergence of girih tiles By 11th century, the Islamic discovered a new way to construct the “tile mosaic” due to the development of arithmetic calculation and geomet ... [...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. It is defined such that one radian is the angle subtended at the centre of a circle by an Circular arc, arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless unit, dimensionless SI derived unit,: "The CGPM decided to interpret the supplementary units in the SI, namely the radian and the steradian, as dimensionless derived units." defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as . Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing. Definition One radian is defined as the angle at the center of a circle in a plane that wikt:subtend, subtends an arc whose length equals the radius of the circle. More generally, the magnit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gothic Architecture
Gothic architecture is an architectural style that was prevalent in Europe from the late 12th to the 16th century, during the High Middle Ages, High and Late Middle Ages, surviving into the 17th and 18th centuries in some areas. It evolved from Romanesque architecture and was succeeded by Renaissance architecture. It originated in the Île-de-France and Picardy regions of northern France. The style at the time was sometimes known as ''opus Francigenum'' (); the term ''Gothic'' was first applied contemptuously during the later Renaissance, by those ambitious to revive the Classical architecture, architecture of classical antiquity. The defining design element of Gothic architecture is the Pointed arch (architecture), pointed arch. The use of the pointed arch in turn led to the development of the pointed rib vault and flying buttresses, combined with elaborate tracery and stained glass windows. At the Abbey of Basilica of Saint-Denis, Saint-Denis, near Paris, the choir was rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'' is the peer review, 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'' cover the full range of List of academ ... [...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 two-dimensional space, the plane by non-overlapping polygons or other shapes, and a tiling is ''aperiodic'' if it does not contain arbitrarily large Periodic tiling, periodic regions or patches. 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 variants 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 rhombus, rhombi, or two different quadrilaterals called kite (geometry), 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 ma ... [...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, "Crystallography ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a Shape, 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 geometry, 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 Scaling (geometry), 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). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similar
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. Peitgen ''et al.'' explain the concept as such: Since mathematically, a fractal may show s ... [...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 Professorship in Science, 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 previo ... [...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., wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
