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3D Hyperbolastic graph of phytoplankton biomass as a function of nutrient concentration and time. According to stem cell researchers at McGowan Institute for Regenerative Medicine at the University of Pittsburgh, "a newer model [called the hyperbolastic type III or] H3 is a differential equation that also describes the cell growth. This model ...
Growth equations. Like exponential growth and logistic growth, hyperbolic growth is highly nonlinear, but differs in important respects.These functions can be confused, as exponential growth, hyperbolic growth, and the first half of logistic growth are convex functions; however their asymptotic behavior (behavior as input gets large) differs dramatically:
Hyperbola (red): two views of a cone and two Dandelin spheres d 1, d 2. The intersection of an upright double cone by a plane not through the vertex with slope greater than the slope of the lines on the cone is a hyperbola (see diagram: red curve).
A ray through the unit hyperbola x 2 − y 2 = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative (see animated version with comparison with the trigonometric (circular) functions).
A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...
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 ...
A plane with slope less than 1 (1 is the slope of the asymptotes of the generating hyperbola) intersects either in an ellipse or in a point or not at all, A plane with slope equal to 1 containing the origin (midpoint of the hyperboloid) does not intersect H 2 {\displaystyle H_{2}} ,
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed.The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P that are parallel to L. [1]