Hypercycle (vector Format)
Hypercycle may refer to: * Hypercycle (chemistry), a kind of reaction network prominent in a theory of the self-organization of matter * Hypercycle (geometry), a curve in hyperbolic space In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to -1. It is homogeneous, and satisfies the stronger property of being a symmetric space. ...

Hypercycle (chemistry)
In chemistry, a hypercycle is an abstract model of organization of self-replicating molecules connected in a Periodic sequence, cyclic, Autocatalysis, autocatalytic manner. It was introduced in an ordinary differential equation (ODE) form by the List of Nobel laureates in Chemistry, Nobel Prize in Chemistry winner Manfred Eigen in 1971 and subsequently further extended in collaboration with Peter Schuster. It was proposed as a solution to the error threshold problem encountered during modelling of replicative molecules that hypothetically existed on the primordial Earth (see: abiogenesis). As such, it explained how life on Earth could have begun using only relatively short Genetic code, genetic sequences, which in theory were too short to store all essential information. The hypercycle is a special case of the replicator equation. The most important properties of hypercycles are autocatalytic growth competition between cycles, once-for-ever selective behaviour, utilization of small ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Hypercycle (geometry)
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis). Given a straight line and a point not on , one can construct a hypercycle by taking all points on the same side of as , with perpendicular distance to equal to that of . The line is called the ''axis'', ''center'', or ''base line'' of the hypercycle. The lines perpendicular to , which are also perpendicular to the hypercycle, are called the '' normals'' of the hypercycle. The segments of the normals between and the hypercycle are called the ''radii''. Their common length is called the ''distance'' or ''radius'' of the hypercycle. The hypercycles through a given point that share a tangent through that point converge towards a horocycle as their distances go towards infinity. Properties similar to those of Euclidean lines Hypercycles in hyperbolic geometry have some properties similar to those of lines in ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]