name the geometry in which each of the following models are used.... sphere, the plane and the pseudoshere?
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sphere, elliptic, plane, euclidean, pseudosphere, hyperbolic
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The pentagon.\nActually any building is technically geometric.
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two circles, in parallel planes with the line connecting their centers forming right-angles with each plane in all directions. ... and the walls comprising the set of line segments one of whose end points is on one circel and the other end point on the other circle withe the property that the segments at each point on circle(A) is the minimum distance to circle(B).\n\n.. or, since you use the word "cylinder" in the question:\n\na cylinder, each of whose end-faces is a circle.
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It is the coordinate system.  X plane is when y and z are constant, for example.
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Sphere\nCylinder\nCone\nWedge
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Think of the projective plane as the disk with opposite boundary points identified. Let the base point for the fundamental group be the center of the disk. The loop that goes directly across the disk and comes back through the other side is the generator of the fundamental group.\n\nAnother way to see this is to notice that the 2-sphere is the universal cover and is a double cover. Thus the fundamental group has two elements. There is only one group of order two up to isomorphism.
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Check Out This Website!! \n\nGives You Examples And Everything!! \n\nhttp://www.mathleague.com/help/geometry/geometry.htm
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It's been too long for me.\n\nSample many definitions. Go to MATHWORLD.COM (lower case)\n2 geometric figures are CONGRUENT when one gets transformed into the other by isometry.\n\nStay with it.\n\nGRIZZ
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Obviously n=2 is a sphere, and n=1 is plane at 45degrees, and n=0 is a defective case.\n\nYou're talking about some geometric generalization of a sphere, with a non-Cartesian distance function (X^n + Y^n + Z ^n).\n\nFor general integer n>=3, or for non-integer n, I can't see a nice geometric interpretation, other than this:\nIf you set n~2 like say n = 2.1 or 1.9 you get a distorted sphere. For n>2, the sphere will bulge inwards in the 8 regions where X,Y,Z are not close to 0, for n<2 it bulges outwards.\n\nTry plotting it in Matlab or Octave and see.\n\nThings that this is *not*:\n- an n-dimensional hypersphere with n=3 (x^2 + y^2 + z^2 + ...x_n^2 = r^2), since the exponent is always 2\n- a spheroid\n\n\n\nThis is _remotely_ similar to visualizing Diophantine equations or Fermat's Last Theorem, but allowing X,Y,Z to be reals, not just integers, i.e. (X,Y,Z) not restricted to lattice points (also Fermat only had X,Y,R-terms, no Z-term, but similar)?\nVery interesting question, not aware if people have got anywhere.\n\nGood luck and let us know what you find.
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U can see the whole world as Geo-metric figures. The Design of a house by civil Engineer is full of Geometry. Followed by lands Planned to use for building purpose and for Ariel view. And with the help of ice in winters if u go to the north and south pole u can find natural and Man made designs which r Geometric figures which u have mentioned above.\n\n  Geometry is not the different types of angles and triangles it includes figures like cone, circle, cylinders , Pentagon and u can go on  Infinity
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It depends on if you a working in two dimensions or three and if you are working in Euclidean geometry or non-Euclidean geometry.\n\nIn Euclidean plane geometry in two dimensions if the two lines are perpendicular to the same line through two distinct points on that line, they will be parallel.\n\nIf you are in three dimensions  going through two distinct points, they could be parallel if lying in the same plane or not if not in the same plane.\n\nIn non-Euclidean elliptic geometry on the surface of a sphere they would always intersect like longitude lines as they are perpendicular to the equator or latitude lines at different points and all intersect at the north and south poles. \nor \nIn non-Euclidean hyperbolic geometry on the surface of a hyperboloid they would be parallel using an analogy to latitude and longitude lines.
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a) isoceles\nb) hexagon\nc) hemisphere\nD) equilateral\ne) \nf)\nG) sphere or spherical\nh)\ni)\nj) scalene\n\nthese are the ones i know. next time, do your own homework!
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in the plane,\nthere are two kinds of curvature,\nthe regular one, which is the norm of the second derivative, if the curve has unit tangent.\nand the signed curvature, which in addition measures if the first derivative and the second derivative preserve orientation.\ns
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Any on Analytic Geometry. My suggestion is "Analytic Geometry" by Charles Lehmann or "Modern Analytic Geometry" by William Wooton.
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a trapezoid.\n   __\n  /__&#92;
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That depends very much on the type of solid.  Mathematically you need to know a lot about its various dimensions and shape.  \n\nPrevious posters have given the answer for box-like shapes (length * width * height) and a cylinder (Pi*r^2*h).  A sphere is PI * 4/3 * (R ^ 3).  \n\nFor complex items you need calculus as well.\n\nIn physics, dunk it in a tank of water filled to the brim and measure the volume of water it displaces.  This works for any shape, provided it fits in the tank.
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Artist: Escher\nPhysician-Mathematician: Roger Penrose. He studied quasi-regular tessellation which were lately found to describe the structure of quasi-crystals, that is the chemical structure of some artificial metallic leagues.\n\nOh, I was forgetting another contemporary one: Raoul Raba. Made famous by the French mathematical organization of Kangourou, for which he created the logo.