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Klein
Klein may refer to: People * Klein (surname) *Klein (musician) Places * Klein (crater), a lunar feature *Klein, Montana, United States * Klein, Texas, United States * Klein (Ohm), a river of Hesse, Germany, tributary of the Ohm *Klein River, a river in the Western Cape province of South Africa Business * Klein Bikes, a bicycle manufacturer * Klein Tools, a manufacturer * S. Klein, a department store * Klein Modellbahn, an Austrian model railway manufacturer Arts * Klein + M.B.O., an Italian musical group *Klein Award, for comic art * Yves Klein, French artist Mathematics *Klein bottle, an unusual shape in topology * Klein geometry * Klein configuration, in geometry *Klein cubic (other) Klein cubic can refer to: * Klein cubic surface *Klein cubic threefold In algebraic geometry, the Klein cubic threefold is the non-singular cubic threefold in 4-dimensional projective space given by the equation :V^2W+W^2X+X^2Y+Y^2Z+Z^2V =0 \, s ... * Klein graphs, in graph theory * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Bottle
In topology, a branch of mathematics, the Klein bottle () is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. While a Möbius strip is a surface with boundary, a Klein bottle has no boundary. For comparison, a sphere is an orientable surface with no boundary. The concept of a Klein bottle was first described in 1882 by the German mathematician Felix Klein. Construction The following square is a fundamental polygon of the Klein bottle. The idea is to 'glue' together the corresponding red and blue edges with the arrows matching, as in the diagrams below. Note that this is an "abstract" gluing in the sense that trying to realize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein, Montana
Klein is a census-designated place (CDP) in Musselshell County, Montana, United States. The population was 188 at the 2000 census. Geography Klein is located at (46.402844, -108.548378). According to the United States Census Bureau, the CDP has a total area of , all of it land. Demographics As of the census of 2000, there were 188 people, 69 households, and 52 families residing in the CDP. The population density was 14.6 people per square mile (5.6/km2). There were 90 housing units at an average density of 7.0/sq mi (2.7/km2). The racial makeup of the CDP was 95.21% White, 3.19% Native American, 1.06% Pacific Islander, and 0.53% from two or more races. Hispanic or Latino of any race were 1.06% of the population. There were 69 households, out of which 30.4% had children under the age of 18 living with them, 65.2% were married couples living together, 7.2% had a female householder with no husband present, and 24.6% were non-families. 18.8% of all households were made up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Bikes
Klein was a bicycle company founded by Gary Klein that pioneered the use of large diameter aluminium alloy tubes for greater stiffness and lower weight. Klein produced his first bicycle frames while a student at the Massachusetts Institute of Technology during the 1970s, and full production runs of frames began in the 1980s. In 1995 the company was purchased by the Trek Bicycle Corporation, and the original Klein factory at Chehalis, Washington, closed in 2002 as production moved to the Trek headquarters at Waterloo, Wisconsin. Widespread distribution in the United States stopped in 2007, and ceased altogether in the rest of the world in 2009. History Gary Klein, born , attended the University of California at Davis before transferring to the Massachusetts Institute of Technology (MIT). During the Independent Activities Period in 1973, a group of students including Klein worked together under Professor Buckley to produce an aluminum framed bicycle. After analyzing a number o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Graphs
In the mathematics, mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in the orientable Surface (topology), surface of Surface (topology)#Classification_of_closed_surfaces, genus 3, in which they form dual graphs. The cubic Klein graph This is a 3-regular graph, regular (Cubic graph, cubic) graph with 56 vertices and 84 edges, named after Felix Klein. It is Hamiltonian graph, Hamiltonian, has chromatic number 3, chromatic index 3, radius 6, diameter 6 and girth (graph theory), girth 7. It is also a 3-k-vertex-connected graph, vertex-connected and a 3-k-edge-connected graph, edge-connected graph. It has book thickness 3 and queue number 2. It can be embedded in the Manifold#Genus_and_the_Euler_characteristic, genus-3 orientable Manifold, surface (which can be represented as the Klein quartic), where it forms the Klein map with 24 heptagonal faces, Schläfli symbol 8. According to the ''Fost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Configuration
In geometry, the Klein configuration, studied by , is a geometric configuration related to Kummer surface In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety o ...s that consists of 60 points and 60 planes, with each point lying on 15 planes and each plane passing through 15 points. The configurations uses 15 pairs of lines, 12 . 13 . 14 . 15 . 16 . 23 . 24 . 25 . 26 . 34 . 35 . 36 . 45 . 46 . 56 and their reverses. The 60 points are three concurrent lines forming an odd permutation, shown below. The sixty planes are 3 coplanar lines forming even permutations, obtained by reversing the last two digits in the points. For any point or plane there are 15 members in the other set containing those 3 lines. udson, 1905 Coordinates of points and planes A possible set of coordinates for points ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleine
Kleine is a German and Dutch surname meaning "small". Notable people with the surname include: * Andrea Kleine (born 1970), American writer, choreographer, and performance artist * Christian Kleine (born 1974), German musician and DJ * Cindy Kleine (born ), American film director, producer and video artist * George Kleine (1864–1931), American film producer and pioneer * Hal Kleine (1923–1957), American baseball pitcher * Joe Kleine (born 1962), American basketball player * Lil' Kleine (born 1994), stage name of Jorik Scholten (born 1994), Dutch rapper * Megan Kleine (born 1974), American swimmer * Piet Kleine (born 1951), Dutch speed skater * Robert Kleine (born 1941), American Michigan State Treasurer * Theodor Kleine (1924–2014), German sprint canoer * Thomas Kleine (born 1977), German football defender and manager See also * Klein (surname) * Kleijn Kleijn is a Dutch surname meaning "small". The ij digraph is often replaced with a "y" (''Kleyn''). [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Garry Stewart
Garry Stewart (born 1962) is an Australian dancer and choreographer. He was the longest-serving artistic director of the Australian Dance Theatre, taking over from Meryl Tankard in 1999 and finishing his term at the end of 2021. He is renowned for his unusual, post-modern interpretations of classical ballets. Early life and education Garry Stewart was born in 1962. After abandoning his university studies in social work when he was 20, Stewart studied first in Sydney at the Sydney City Ballet Academy (1983), and then at the Australian Ballet School in Melbourne (1984–1985). Dance career He has danced with the Australian Dance Theatre (ADT), the Queensland Ballet, Expressions Dance Company and The One Extra Dance Company (Onex), and has performed in acting roles with the Sydney Theatre Company. He also worked on many independent projects, and in 1989 performed the role of Luke in production of ''Harold in Italy''. He retired from professional dancing at the end of the 1980 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Technique
Klein may refer to: People *Klein (surname) *Klein (musician) Places *Klein (crater), a lunar feature *Klein, Montana, United States *Klein, Texas, United States *Klein (Ohm), a river of Hesse, Germany, tributary of the Ohm *Klein River, a river in the Western Cape province of South Africa Business *Klein Bikes, a bicycle manufacturer *Klein Tools, a manufacturer *S. Klein, a department store *Klein Modellbahn, an Austrian model railway manufacturer Arts *Klein + M.B.O., an Italian musical group * Klein Award, for comic art *Yves Klein, French artist Mathematics *Klein bottle, an unusual shape in topology *Klein geometry *Klein configuration, in geometry * Klein cubic (other) *Klein graphs, in graph theory *Klein model, or Beltrami–Klein model, a model of hyperbolic geometry *Klein polyhedron, a generalization of continued fractions to higher dimensions, in the geometry of numbers *Klein surface, a dianalytic manifold of complex dimension 1 Other uses * Kleins, Line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lineman's Pliers
Lineman's pliers (US English), Kleins (genericized trademark, US usage), linesman pliers (Canadian English), side cutting linesman pliers and combination pliers (UK / US English) are a type of pliers used by linemen, electricians, and other tradesmen primarily for gripping, twisting, bending and cutting wire, cable and small metalwork components. They owe their effectiveness to their plier design, which multiplies force through leverage. Lineman's pliers are distinguished by a flat gripping surface at their snub nose. Combination pliers have a shorter flat surface plus a concave / curved gripping surface which is useful in light engineering to work with metal bar, etc. Both usually have a bevelled cutting edge similar to that on Diagonal pliers in their craw, and each may include an additional gripping, crimping, or wire shearing (for a flat ended cut) device at the crux of the handle side of the pliers' joint. Designed for potentially heavy manual operation, these pliers typica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Surface
In mathematics, a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein surfaces generalize Riemann surfaces. While the latter are used to study algebraic curves over the complex numbers analytically, the former are used to study algebraic curves over the real numbers analytically. Klein surfaces were introduced by Felix Klein in 1882. A Klein surface is a surface (i.e., a differentiable manifold of real dimension 2) on which the notion of angle between two tangent vectors at a given point is well-defined, and so is the angle between two intersecting curves on the surface. These angles are in the range ,π since the surface carries no notion of orientation, it is not possible to distinguish between the angles α and −α. (By contrast, on Riemann surfaces are oriented and angles in the range of (-π,π] can be meaningfully defined.) The length of curves, the area of submanifolds and the notion of ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Polyhedron
In the geometry of numbers, the Klein polyhedron, named after Felix Klein, is used to generalize the concept of continued fractions to higher dimensions. Definition Let \textstyle C be a closed simplicial cone in Euclidean space \textstyle \mathbb^n. The ''Klein polyhedron'' of \textstyle C is the convex hull of the non-zero points of \textstyle C \cap \mathbb^n. Relation to continued fractions Suppose \textstyle \alpha > 0 is an irrational number. In \textstyle \mathbb^2, the cones generated by \textstyle \ and by \textstyle \ give rise to two Klein polyhedra, each of which is bounded by a sequence of adjoining line segments. Define the ''integer length'' of a line segment to be one less than the size of its intersection with \textstyle \mathbb^n. Then the integer lengths of the edges of these two Klein polyhedra encode the continued-fraction expansion of \textstyle \alpha, one matching the even terms and the other matching the odd terms. Graphs associated with the Klein p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klein Model
Klein may refer to: People *Klein (surname) *Klein (musician) Places *Klein (crater), a lunar feature *Klein, Montana, United States *Klein, Texas, United States *Klein (Ohm), a river of Hesse, Germany, tributary of the Ohm *Klein River, a river in the Western Cape province of South Africa Business *Klein Bikes, a bicycle manufacturer *Klein Tools, a manufacturer *S. Klein, a department store *Klein Modellbahn, an Austrian model railway manufacturer Arts *Klein + M.B.O., an Italian musical group * Klein Award, for comic art *Yves Klein, French artist Mathematics *Klein bottle, an unusual shape in topology *Klein geometry *Klein configuration, in geometry * Klein cubic (other) *Klein graphs, in graph theory *Klein model, or Beltrami–Klein model, a model of hyperbolic geometry *Klein polyhedron, a generalization of continued fractions to higher dimensions, in the geometry of numbers *Klein surface, a dianalytic manifold of complex dimension 1 Other uses * Kleins, Line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
