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An x value where the y value of the red, or the blue, curve vanishes (becomes 0) gives rise to a local extremum (marked "HP", "TP"), or an inflection point ("WP"), of the black curve, respectively. In geometry , curve sketching (or curve tracing ) are techniques for producing a rough idea of overall shape of a plane curve given its equation ...
Download as PDF; Printable version; In other projects ... move to sidebar hide. This is a gallery of curves used in mathematics, by Wikipedia page. See also ...
Download as PDF; Printable version; In other projects ... This is a list of Wikipedia articles about curves used in different fields: mathematics (including ...
An example is the Fermat curve u n + v n = w n, which has an affine form x n + y n = 1. A similar process of homogenization may be defined for curves in higher dimensional spaces. Except for lines, the simplest examples of algebraic curves are the conics, which are nonsingular curves of degree two and genus zero.
curve sketching In geometry, curve sketching (or curve tracing) includes techniques that can be used to produce a rough idea of overall shape of a plane curve given its equation without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features. Here input is an ...
A simple example of a point of inflection is the function f(x) = x 3. There is a clear change of concavity about the point x = 0, and we can prove this by means of calculus. The second derivative of f is the everywhere-continuous 6x, and at x = 0, f″ = 0, and the sign changes about this point. So x = 0 is a point of inflection.
In addition to curves and surfaces, parametric equations can describe manifolds and algebraic varieties of higher dimension, with the number of parameters being equal to the dimension of the manifold or variety, and the number of equations being equal to the dimension of the space in which the manifold or variety is considered (for curves the ...
Generally, an isocline will itself have the shape of a curve or the union of a small number of curves. Isoclines are often used as a graphical method of solving ordinary differential equations. In an equation of the form y' = f(x, y), the isoclines are lines in the (x, y) plane obtained by setting f(x, y) equal to a constant. This gives a ...
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