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The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...
Geogebra (Geometry and Algebra) - combines geometric objects like circles and graphs of functions with its algebraic representation e.g. + = representing a circle with the radius . Designed for use in schools and educational settings.
There are three main types of computer environments for studying school geometry: supposers [vague], dynamic geometry environments (DGEs) and Logo-based programs. [2] Most are DGEs: software that allows the user to manipulate ("drag") the geometric object into different shapes or positions.
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation" [3]) is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentiable manifolds, numerical analysis, number theory, calculus and statistics.
The inverse function only produces numerical values in the set of real numbers between its two asymptotes, which are now vertical instead of horizontal like in the forward Gompertz function. Outside of the range defined by the vertical asymptotes, the inverse function requires computing the logarithm of negative numbers.
An illustrative example is the derivation of the boundary layer equations from the full Navier-Stokes equations governing fluid flow. In many cases, the asymptotic expansion is in power of a small parameter, ε : in the boundary layer case, this is the nondimensional ratio of the boundary layer thickness to a typical length scale of the problem.
Asymptote is a descriptive vector graphics language – developed by Andy Hammerlindl, John C. Bowman (University of Alberta), and Tom Prince – which provides a natural coordinate-based framework for technical drawing. Asymptote runs on all major platforms (Unix, Mac OS, Microsoft Windows).
In the history of mathematics, it is remembered as one of the first examples of Isaac Barrow's application of rudimentary calculus methods to determine the tangent of a curve. Isaac Newton and Johann Bernoulli continued the studies of this curve subsequently. Using the Cartesian coordinate system it can be expressed as