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Arnold's Rouble Problem
The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring to Vladimir Arnold and the folding of a Russian ruble bank note. Some versions of the problem were solved by Robert J. Lang, Svetlana Krat, Alexey S. Tarasov, and Ivan Yaschenko. One form of the problem remains open. Formulations There are several way to define the notion of folding, giving different interpretations. By convention, the napkin is always a unit square. Folding along a straight line Considering the folding as a reflection along a line that reflects all the layers of the napkin, the perimeter is always non-increasing, thus never exceeding 4. By considering more general foldings that possibly reflect only a single layer of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Origami
) is the Japanese paper art, art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word ' to refer to designs which use cuts. On the other hand, in the detailed Japanese classification, origami is divided into stylized ceremonial origami (儀礼折り紙, ''girei origami'') and recreational origami (遊戯折り紙, ''yūgi origami''), and only recreational origami is generally recognized as origami. In Japan, ceremonial origami is generally called "origata" (:ja:折形) to distinguish it from recreational origami. The term "origata" is one of the old terms for origami. The small number of basic Origami techniques, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Igor Pak
Igor Pak (russian: link=no, Игорь Пак) (born 1971, Moscow, Soviet Union) is a professor of mathematics at the University of California, Los Angeles, working in combinatorics and discrete probability. He formerly taught at the Massachusetts Institute of Technology and the University of Minnesota, and he is best known for his bijective proof of the Young tableau#Dimension of a representation, hook-length formula for the number of Young tableaux, and his work on random walks. He was a keynote speaker alongside George Andrews (mathematician), George Andrews and Doron Zeilberger at the 2006 Harvey Mudd College Mathematics Conference on Enumerative Combinatorics. Pak is an Associate Editor for the journal Discrete Mathematics (journal), ''Discrete Mathematics''. He gave a László Fejes Tóth, Fejes Tóth Lecture at the University of Calgary in February 2009. In 2018, he was an List of International Congresses of Mathematicians Plenary and Invited Speakers#2018, Rio de Janeiro, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph O'Rourke (professor)
Joseph O'Rourke is the Spencer T. and Ann W. Olin Professor of Computer Science at Smith College and the founding chair of the Smith computer science department. His main research interest is computational geometry. One of O'Rourke's early results was an algorithm for finding the minimum bounding box of a point set in three dimensions when the box is not required to be axis-aligned. The problem is made difficult by the fact that the optimal box may not share any of its face planes with the convex hull of the point set. Nevertheless, O'Rourke found an algorithm for this problem with running time O(n^3). In 1985, O'Rourke was the program chair of the first annual Symposium on Computational Geometry. He was formerly the arXiv moderator for computational geometry and discrete mathematics. In 2012 O'Rourke was named a Fellow of the Association for Computing Machinery A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erik Demaine
Erik D. Demaine (born February 28, 1981) is a professor of computer science at the Massachusetts Institute of Technology and a former child prodigy. Early life and education Demaine was born in Halifax, Nova Scotia, to artist sculptor Martin L. Demaine and Judy Anderson. From the age of 7, he was identified as a child prodigy and spent time traveling across North America with his father. He was home-schooled during that time span until entering university at the age of 12. Demaine completed his bachelor's degree at 14 years of age at Dalhousie University in Canada, and completed his PhD at the University of Waterloo by the time he was 20 years old. Demaine's PhD dissertation, a work in the field of computational origami, was completed at the University of Waterloo under the supervision of Anna Lubiw and Ian Munro. This work was awarded the Canadian Governor General's Gold Medal from the University of Waterloo and the NSERC Doctoral Prize (2003) for the best PhD thesis an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A K Peters
A K Peters, Ltd. was a publisher of scientific and technical books, specializing in mathematics and in computer graphics, robotics, and other fields of computer science. They published the journals ''Experimental Mathematics'' and the '' Journal of Graphics Tools'', as well as mathematics books geared to children. Background Klaus Peters wrote a doctoral dissertation on complex manifolds at the University of Erlangen in 1962, supervised by Reinhold Remmert. He then joined Springer Verlag, becoming their first specialist mathematics editor. As a Springer director from 1971, he hired Alice Merker for Springer New York: they were married that year, and moved to Heidelberg. Leaving Springer, they founded Birkhäuser Boston in 1979; Birkhäuser ran into financial difficulties, and was taken over by Springer. Klaus and Alice then spent a period running a Boston office for Harcourt Brace Jovanovich and their imprint Academic Press. With the takeover of Harcourt Brace Jovanovich by Gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books in the public domain. The original published editions may be scarce or historically significant. Dover republishes these books, making them available at a significantly reduced cost. Classic reprints Dover reprints classic works of literature, classical sheet music, and public-domain images from the 18th and 19th centuries. Dover also publishes an extensive collection of mathematical, scientific, and engineering texts. It often targets its reprints at a niche market, such as woodworking. Starting in 2015, the company branched out into graphic novel reprints, overseen by Dover acquisitions editor and former comics writer and editor Drew Ford. Most Dover reprints are photo facsimiles of the originals, retaining the original pagination and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mathematical Intelligencer
''The Mathematical Intelligencer'' is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released quarterly with a subset of open access articles. Springer also cross-publishes some of the articles in ''Scientific American''. Karen Parshall and Sergei Tabachnikov are currently the co-editors-in-chief. History The journal was started informally in 1971 by Walter Kaufman-Buehler, Alice Peters and Klaus Peters. "Intelligencer" was chosen by Kaufman-Buehler as a word that would appear slightly old-fashioned. An exploration of mathematically themed stamps, written by Robin Wilson, became one of its earliest columns. In 1978, the founders appointed Bruce Chandler and Harold "Ed" Edwards Jr. to serve jointly in the role of editor-in-chief. Prior to 1978, articles of the ''Intelligencer'' were not contained in regular volumes and were sent out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Folklore
Folklore is shared by a particular group of people; it encompasses the traditions common to that culture, subculture or group. This includes oral traditions such as tales, legends, proverbs and jokes. They include material culture, ranging from traditional building styles common to the group. Folklore also includes customary lore, taking actions for folk beliefs, the forms and rituals of celebrations such as Christmas and weddings, folk dances and initiation rites. Each one of these, either singly or in combination, is considered a folklore artifact or traditional cultural expression. Just as essential as the form, folklore also encompasses the transmission of these artifacts from one region to another or from one generation to the next. Folklore is not something one can typically gain in a formal school curriculum or study in the fine arts. Instead, these traditions are passed along informally from one individual to another either through verbal instruction or demonstr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newsgroup
A Usenet newsgroup is a repository usually within the Usenet system, for messages posted from users in different locations using the Internet. They are discussion groups and are not devoted to publishing news. Newsgroups are technically distinct from, but functionally similar to, discussion forums on the World Wide Web. Newsreader software is used to read the content of newsgroups. Before the adoption of the World Wide Web, Usenet newsgroups were among the most popular Internet services, and have retained their noncommercial nature in contrast to the increasingly ad-laden web. In recent years, this form of open discussion on the Internet has lost considerable ground to individually-operated browser-accessible forums and big media social networks such as Facebook and Twitter. Communication is facilitated by the Network News Transfer Protocol (NNTP) which allows connection to Usenet servers and data transfer over the internet. Similar to another early (yet still used) protocol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jim Propp
James Gary Propp is a professor of mathematics at the University of Massachusetts Lowell. Education and career In high school, Propp was one of the national winners of the United States of America Mathematical Olympiad (USAMO), and an alumnus of the Hampshire College Summer Studies in Mathematics. Propp obtained his AB in mathematics in 1982 at Harvard. After advanced study at Cambridge, he obtained his PhD from the University of California at Berkeley. He has held professorships at seven universities, including Harvard, MIT, the University of Wisconsin, and the University of Massachusetts Lowell. Mathematical research Propp is the co-editor of the book ''Microsurveys in Discrete Probability'' (1998) and has written more than fifty journal articles on game theory, combinatorics and probability, and recreational mathematics. He lectures extensively and has served on the Mathematical Olympiad Committee of the Mathematical Association of America, which sponsors the USAMO. In the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sea Urchin
Sea urchins () are spiny, globular echinoderms in the class Echinoidea. About 950 species of sea urchin live on the seabed of every ocean and inhabit every depth zone from the intertidal seashore down to . The spherical, hard shells (tests) of sea urchins are round and spiny, ranging in diameter from . Sea urchins move slowly, crawling with tube feet, and also propel themselves with their spines. Although algae are the primary diet, sea urchins also eat slow-moving (sessile) animals. Predators that eat sea urchins include a wide variety of fish, starfish, crabs, marine mammals. Sea urchins are also used as food especially in Japan. Adult sea urchins have fivefold symmetry, but their pluteus larvae feature bilateral (mirror) symmetry, indicating that the sea urchin belongs to the Bilateria group of animal phyla, which also comprises the chordates and the arthropods, the annelids and the molluscs, and are found in every ocean and in every climate, from the tropics to the pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
