Pleated Manifold
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Pleated Manifold
In geometry, a pleated surface is roughly a surface that may have simple folds but is not crumpled in more complicated ways. More precisely, a pleated surface is an isometry from a complete hyperbolic surface ''S'' to a hyperbolic 3-fold such that every point of ''S'' is in the interior of a geodesic that is mapped to a geodesic. They were introduced by , where they were called uncrumpled surfaces. The Universal Book of Mathematics ''The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes'' (2004) is a bestselling book by British author David Darling (astronomer), David Darling. Summary The book is presented in a dictionary format. The book is divided into ... provides the following information about pleated surfaces: ''It is a surface in Euclidean space or hyperbolic space that resembles a polyhedron in the sense that it has flat faces that meet along edges. Unlike a polyhedron, a pleated surface has no corners, but it may have infinite ...
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Knife Pleat
A pleat (plait in older English) is a type of fold formed by doubling fabric back upon itself and securing it in place. It is commonly used in clothing and upholstery to gather a wide piece of fabric to a narrower circumference. Pleats are categorized as ''pressed'', that is, ironed or otherwise heat-set into a sharp crease, or ''unpressed'', falling in soft rounded folds. Pleats sewn into place are called tucks. Types Accordion Accordion pleats or knife pleats are a form of tight pleating which allows the garment to expand its shape when moving. Accordion pleating is also used for some dress sleeves, such as pleating the end of the elbow, with the fullness of the pleat gathered closely at the cuff. This form of pleating inspired the "skirt dancing" of Loie Fuller. Accordion pleats may also be used in hand fans. Box Box pleats are knife pleats back-to-back, and have a tendency to spring out from the waistline.Picken, Mary Brooks, ''The Fashion Dictionary'', p. 257 They ha ...
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Escort Wreck 006
Escort may refer to: Protection *Bodyguard, a security operative who accompanies clients for their personal protection * Police escort, a feature offered by law enforcement agencies to assist in transporting individuals *Safety escort service, a service provided on and around many college and university campuses to help ensure the safety of students and staff *Escort carrier, a small aircraft carrier used in World War II * Escort destroyer, a warship assigned to protect merchant ships in time of war * Escort fighter, a World War II concept for a fighter aircraft designed to escort bombers * Escort vehicle, a vehicle that escorts oversize trucks or large vehicle convoys on highways Arts and media Film * ''The Escort'' (1993 film), an Italian film directed by Ricky Tognazzi * ''The Escort'' (1996 film), a Canadian film directed by Denis Langlois * ''The Escort'' (1997 film), an American film directed by Gary Graver * ''Escort'' (2001 film), a Chinese film directed by Qi Xing * ''Esc ...
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The Universal Book Of Mathematics
''The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes'' (2004) is a bestselling book by British author David Darling (astronomer), David Darling. Summary The book is presented in a dictionary format. The book is divided into headwords, which, as the title suggests, run from Abracadabra to Zeno's paradoxes. The book also provides relevant diagrams and illustrations. Errors The first edition of the book had several errors which were fixed in later editions. Several famous scientists have sent in corrections to the David Darling (astronomer), author of the book. These include Warren Johnson and Freeman Dyson. Reception The book has been praised by BoingBoing and British newspaper ''The Independent''. Problems and Puzzles mentioned in the book have been discussed and debated several times by several major mathematicians. See also * David Darling (astronomer) * Mathematics References External linksboingboing.com
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Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ...
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Hyperbolic Geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' not on ''R'', in the plane containing both line ''R'' and point ''P'' there are at least two distinct lines through ''P'' that do not intersect ''R''. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane. A modern use of hyperbolic geometry is in the theory of special relativity, particularly the Minkowski model. When geometers first realised they were working with something other than the standard Euclidean geometry, they described their geomet ...
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