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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 filmmaking technique whereby image, still images are manipulated to create Motion picture, moving images. In traditional animation, images are drawn or painted by hand on cel, transparent celluloid sheets to be photographed and exhibited on film. Animation has been recognised as an artistic medium, specifically within the Entertainment#Industry, entertainment industry. Many animations are either traditional animations or computer animations made with computer-generated imagery (CGI). Stop motion animation, in particular claymation, has continued to exist alongside these other forms. Animation is contrasted with live action, although the two do not exist in isolation. Many moviemakers have produced Live-action animation, films that are a hybrid of the two. As CGI increasingly Photorealism, approximates photographic imagery, filmmakers can easily Compositing, composite 3D animations into their film rather than using practical effects for showy visual effects (VFX). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. 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 (mathematics), 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 can occur. A process that exhibits recursion is ''recursive''. Video feedback displays recursive images, as does an infinity mirror. 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 reduce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric W
The given name Eric, Erich, Erikk, Erik, Erick, Eirik, or Eiríkur 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 new ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dutch People
The Dutch, or Netherlanders (Dutch language, Dutch: ) are an ethnic group native to the Netherlands. They share a common ancestry and culture and speak the Dutch language. Dutch people and their descendants are found in migrant communities worldwide, notably in Argentina, Aruba, Australia, Brazil, Canada,Based on Statistics Canada, Canada 2001 Census]Linkto Canadian statistics. Caribbean Netherlands, Curaçao, Germany, Guyana, Indonesia, New Zealand, Sint Maarten, South Africa, Suriname, 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 ... [...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 three regular and eight 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, construc ... [...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 iterated function, 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 sq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
