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Pythagoras Tree (fractal)
The Pythagoras tree is a Plane (geometry), plane fractal constructed from Square (geometry), squares. Invented by the Netherlands, Dutch mathematics teacher Albert E. Bosman in 1942, it is named after the Ancient Greece, ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem. If the largest square has a size of ''L'' × ''L'', the entire Pythagoras tree fits snugly inside a box of size 6''L'' × 4''L''.Wisfaq.nl The finer details of the tree resemble the Lévy C curve. Construction The construction of the Pythagoras tree begins with a square (geometry), square. Upon this square are constructed two squares, each scaled down by a linear ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Animated Self-resembling Pythagoras Tree (fractal)
Animation is a method by which image, still figures are manipulated to appear as Motion picture, moving images. In traditional animation, images are drawn or painted by hand on transparent cel, celluloid sheets to be photographed and exhibited on film. Today, most animations are made with computer-generated imagery (CGI). Computer animation can be very detailed Computer animation#Animation methods, 3D animation, while Traditional animation#Computers and traditional animation, 2D computer animation (which may have the look of traditional animation) can be used for stylistic reasons, low bandwidth, or faster real-time renderings. Other common animation methods apply a stop motion technique to two- and three-dimensional objects like cutout animation, paper cutouts, puppets, or Clay animation, clay figures. A cartoon is an animated film, usually a short film, featuring an cartoon, exaggerated visual style. The style takes inspiration from comic strips, often featuring anthropomorphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references ("crock recursion") can occur. Formal definitions In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: * A simple ''base case'' (or cases) — a terminating scenario that does not use recursion to produce an answer * A ''recursive step'' — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ''ancestor''. One's ances ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric W
The given name Eric, Erich, Erikk, Erik, Erick, or Eirik is derived from the Old Norse name ''Eiríkr'' (or ''Eríkr'' in Old East Norse due to monophthongization). The first element, ''ei-'' may be derived from the older Proto-Norse ''* aina(z)'', meaning "one, alone, unique", ''as in the form'' ''Æ∆inrikr'' explicitly, but it could also be from ''* aiwa(z)'' "everlasting, eternity", as in the Gothic form ''Euric''. The second element ''- ríkr'' stems either from Proto-Germanic ''* ríks'' "king, ruler" (cf. Gothic ''reiks'') or the therefrom derived ''* ríkijaz'' "kingly, powerful, rich, prince"; from the common Proto-Indo-European root * h₃rḗǵs. The name is thus usually taken to mean "sole ruler, autocrat" or "eternal ruler, ever powerful". ''Eric'' used in the sense of a proper noun meaning "one ruler" may be the origin of ''Eriksgata'', and if so it would have meant "one ruler's journey". The tour was the medieval Swedish king's journey, when newly elected, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dutch People
The Dutch (Dutch: ) are an ethnic group and nation native to the Netherlands. They share a common history and culture and speak the Dutch language. Dutch people and their descendants are found in migrant communities worldwide, notably in Aruba, Suriname, Guyana, Curaçao, Argentina, Brazil, Canada,Based on Statistics Canada, Canada 2001 Censusbr>Linkto Canadian statistics. Australia, South Africa, New Zealand and the United States.According tFactfinder.census.gov The Low Countries were situated around the border of France and the Holy Roman Empire, forming a part of their respective peripheries and the various territories of which they consisted had become virtually autonomous by the 13th century. Under the Habsburgs, the Netherlands were organised into a single administrative unit, and in the 16th and 17th centuries the Northern Netherlands gained independence from Spain as the Dutch Republic. The high degree of urbanization characteristic of Dutch society was attained at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhombitrihexagonal Tiling
In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one triangle, two squares, and one hexagon on each vertex. It has Schläfli symbol of rr. John Conway calls it a rhombihexadeltille.Conway, 2008, p288 table It can be considered a cantellated by Norman Johnson's terminology or an expanded hexagonal tiling by Alicia Boole Stott's operational language. There are 3 regular and 8 semiregular tilings in the plane. Uniform colorings There is only one uniform coloring in a rhombitrihexagonal tiling. (Naming the colors by indices around a vertex (3.4.6.4): 1232.) With edge-colorings there is a half symmetry form (3*3) orbifold notation. The hexagons can be considered as truncated triangles, t with two types of edges. It has Coxeter diagram , Schläfli symbol s2. The bicolored square can be distorted into isosceles trapezoids. In the limit, where the rectangles degenerate into edges, a triangular tiling results, constructed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iteration
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
