one-dimensional torus

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• One-dimensional symmetry group — A one dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x. The 1D isometries map x to x + a and to a − x.… …   Wikipedia

• Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …   Wikipedia

• Torus bundle — In mathematics, in the sub field of geometric topology, a torus bundle is a kind of surface bundle over the circle, which in turn are a class of three manifolds.ConstructionTo obtain a torus bundle: let f be an orientation preserving… …   Wikipedia

• One-parameter group — In mathematics, a one parameter group or one parameter subgroup usually means a continuous group homomorphism φ : R → G from the real line R (as an additive group) to some other topological group G. That means that it is not in fact a group …   Wikipedia

• Algebraic torus — In mathematics, an algebraic torus is a type of commutative affine algebraic group. These groups were named by analogy with the theory of tori in Lie group theory (see maximal torus). The theory of tori is in some sense opposite to that of… …   Wikipedia

• Triple torus — or three torus can refer to one of the two following concepts, both related to a torus.Three dimensional torusThe three dimensonal torus, or triple torus, is defined as the Cartesian product of three circles, :mathbb{T}^3 = S^1 imes S^1 imes… …   Wikipedia

• n-dimensional sequential move puzzle — Five dimensional 25 puzzle partial cutaway demonstrating that even with the minimum size in 5 D the puzzle is far from trivial. The 4 D nature of the stickers is clearly visible in this screen shot. The Rubik s cube is the original and best known …   Wikipedia

• Maximal torus — In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a Lie group G is a compact, connected, abelian Lie subgroup of G (and therefore isomorphic to… …   Wikipedia

• Umbilic torus — Created by Helaman Ferguson, the umbilic torus is a single edged 3 dimensional figure. Ferguson created a 27 inch bronze sculpture, Umbilic Torus, and it is his most widely known piece of art. The torus blurs the distinction between mathematics… …   Wikipedia

• Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …   Wikipedia

• Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia