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Asymptote. The graph of a function with a horizontal ( y = 0), vertical ( x = 0), and oblique asymptote (purple line, given by y = 2 x ). A curve intersecting an asymptote infinitely many times. In analytic geometry, an asymptote ( / ˈæsɪmptoʊt /) of a curve is a line such that the distance between the curve and the line approaches zero as ...
An asymptotic direction is a direction along which the normal curvature is zero: take the plane spanned by the direction and the surface's normal at that point. The curve of intersection of the plane and the surface has zero curvature at that point. An asymptotic curve is a curve such that, at each point, the plane tangent to the surface is an ...
Asymptotic analysis. In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared ...
Truncus (mathematics) In analytic geometry, a truncus is a curve in the Cartesian plane consisting of all points ( x, y) satisfying an equation of the form. A mathematical graph of the basic truncus formula, marked in blue, with domain and range both restricted to [-5, 5]. where a , b, and c are given constants.
The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting. In the plane the equation is. If we stretch the curve in the direction by a factor of this becomes which is ...
In algebraic geometry, a non singular point of an algebraic curve is an inflection point if and only if the intersection number of the tangent line and the curve (at the point of tangency) is greater than 2. The main motivation of this different definition, is that otherwise the set of the inflection points of a curve would not be an algebraic set.
The general equation's coefficients can be obtained from known semi-major axis , semi-minor axis , center coordinates (,), and rotation angle (the angle from the positive horizontal axis to the hyperbola's major axis) using the formulae:
Newton's diagram. Newton's diagram (also known as Newton's parallelogram, after Isaac Newton) is a technique for determining the shape of an algebraic curve close to and far away from the origin. It consists of plotting (α, β) for each term Axαyβ in the equation of the curve. The resulting diagram is then analyzed to produce information ...