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The Fractal Geometry Of Nature
''The Fractal Geometry of Nature'' is a 1982 book by the Franco-American mathematician Benoît Mandelbrot. Overview ''The Fractal Geometry of Nature'' is a revised and enlarged version of his 1977 book entitled ''Fractals: Form, Chance and Dimension'', which in turn was a revised, enlarged, and translated version of his 1975 French book, ''Les Objets Fractals: Forme, Hasard et Dimension''. '' American Scientist'' put the book in its one hundred books of 20th century science. As technology has improved, mathematically accurate, computer-drawn fractals 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 scale ... have become more detailed. Early drawings were low-resolution black and white; later drawings were higher resolution and in color. Many examples were created by programmers working w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benoît Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of #Fractals and the "theory of roughness", roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having Multiple citizenship, dual French nati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodreads
Goodreads is an American social cataloging website and a subsidiary of Amazon that allows individuals to search its database of books, annotations, quotes, and reviews. Users can sign up and register books to generate library catalogs and reading lists. They can also create their own groups of book suggestions, surveys, polls, blogs, and discussions. The website's offices are located in San Francisco. Goodreads was founded in December 2006 and launched in January 2007 by Otis Chandler and Elizabeth Khuri Chandler. In December 2007, the site had 650,000 members and 10,000,000 books had been added. By July 2012, the site reported 10 million members, 20 million monthly visits, and thirty employees. On March 28, 2013, Amazon announced its acquisition of Goodreads, and by July 23, 2013, Goodreads announced their user base had grown to 20 million members. By September 2023, the site had more than 150 million members. History Founders Goodreads founders Otis Chandler and Elizabeth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Scientist
''American Scientist'' (informally abbreviated ''AmSci'') is an American bimonthly science and technology magazine published since 1913 by Sigma Xi, The Scientific Research Honor Society. In the beginning of 2000s the headquarters was moved to Research Triangle Park, (Durham), North Carolina. Each issue includes feature articles written by scientists and engineers who review research in fields from molecular biology to computer engineering. Each issue also includes the work of cartoonist A cartoonist is a visual artist who specializes in both drawing and writing cartoons (individual images) or comics (sequential images). Cartoonists differ from comics writers or comics illustrators/artists in that they produce both the litera ...s, including those of Sidney Harris, Benita Epstein, and Mark Heath. Also included is the ''Scientists' Nightstand'' that reviews a vast range of science-related books and novels. ''American Scientist Online'' () was launched in May 2003. Re ... [...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] |
IBM Research
IBM Research is the research and development division for IBM, an American Multinational corporation, multinational information technology company. IBM Research is headquartered at the Thomas J. Watson Research Center in Yorktown Heights, New York, near IBM headquarters in Armonk, New York. It is the largest industrial research organization in the world with operations in over 170 countries and twelve labs on six continents. IBM employees have garnered six Nobel Prizes, six Turing Awards, 20 inductees into the U.S. National Inventors Hall of Fame, 19 National Medal of Technology, National Medals of Technology, five National Medal of Science, National Medals of Science and three Kavli Foundation (United States)#The Kavli Prize, Kavli Prizes. , the company has generated more patents than any other business in each of 25 consecutive years, which is a record. History The roots of today's IBM Research began with the 1945 opening of the Watson Scientific Computing Laboratory at Columbi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas. Text was copied from this source, which is avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1982 Non-fiction Books
__NOTOC__ Year 198 (CXCVIII) was a common year starting on Sunday of the Julian calendar. At the time, it was known as the Year of the Consulship of Sergius and Gallus (or, less frequently, year 951 ''Ab urbe condita''). The denomination 198 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire *January 28 **Publius Septimius Geta, son of Septimius Severus, receives the title of Caesar. **Caracalla, son of Septimius Severus, is given the title of Augustus. China *Winter – Battle of Xiapi: The allied armies led by Cao Cao and Liu Bei defeat Lü Bu; afterward Cao Cao has him executed. By topic Religion * Marcus I succeeds Olympianus as Patriarch of Constantinople (until 211). Births * Lu Kai, Chinese official and general (d. 269) * Quan Cong, Chinese general and advisor (d. 249) Deaths * Li Jue, Chinese warlord and regent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Books
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstractio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
