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  2. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh( x / a ) is the catenary , the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.

  3. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    Graphs of the inverse hyperbolic functions The hyperbolic functions sinh, cosh, and tanh with respect to a unit hyperbola are analogous to circular functions sin, cos, tan with respect to a unit circle. The argument to the hyperbolic functions is a hyperbolic angle measure.

  4. Hyperbolic geometric graph - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_geometric_graph

    A hyperbolic geometric graph (HGG) or hyperbolic geometric network (HGN) is a special type of spatial network where (1) latent coordinates of nodes are sprinkled according to a probability density function into a hyperbolic space of constant negative curvature and (2) an edge between two nodes is present if they are close according to a function of the metric [1] [2] (typically either a ...

  5. Hyperbolic growth - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_growth

    Another example of hyperbolic growth can be found in queueing theory: the average waiting time of randomly arriving customers grows hyperbolically as a function of the average load ratio of the server. The singularity in this case occurs when the average amount of work arriving to the server equals the server's processing capacity.

  6. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons.

  7. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    Just as the trigonometric functions are defined in terms of the unit circle, so also the hyperbolic functions are defined in terms of the unit hyperbola, as shown in this diagram. In a unit circle, the angle (in radians) is equal to twice the area of the circular sector which that angle subtends.

  8. Hyperbolic coordinates - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_coordinates

    The hyperbolic coordinates are formed on the original picture of G. de Saint-Vincent, which provided the quadrature of the hyperbola, and transcended the limits of algebraic functions. In 1875 Johann von Thünen published a theory of natural wages [ 1 ] which used geometric mean of a subsistence wage and market value of the labor using the ...

  9. Tractrix - Wikipedia

    en.wikipedia.org/wiki/Tractrix

    It is the locus of the center of a hyperbolic spiral rolling (without skidding) on a straight line. It is the involute of the catenary function, which describes a fully flexible, inelastic, homogeneous string attached to two points that is subjected to a gravitational field. The catenary has the equation y(x) = a cosh ⁠ x / a ⁠.

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