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In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface. In all ...
Such a parametric equation completely determines the curve, without the need of any interpretation of t as time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One similarly gets the parametric equation of a surface by considering functions of two parameters t and u.
Graphs of roses are composed of petals.A petal is the shape formed by the graph of a half-cycle of the sinusoid that specifies the rose. (A cycle is a portion of a sinusoid that is one period T = 2π / k long and consists of a positive half-cycle, the continuous set of points where r ≥ 0 and is T / 2 = π / k long, and a negative half-cycle is the other half where r ...
A cusp at (0, 1/2) In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve. For a plane curve defined by an analytic, parametric equation
Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem and the divergence theorem, are frequently given in a parametric form.
The curve is given by the following parametric equations: [2] = ... In 2006, two mathematicians using Mathematica analyzed the function, ...
In calculus, integration by parametric derivatives, also called parametric integration, [1] is a method which uses known Integrals to integrate derived functions. It is often used in Physics, and is similar to integration by substitution.
The orthotomic of a curve is its pedal magnified by a factor of 2 so that the center of similarity is P. This is locus of the reflection of P through the tangent line T. The pedal curve is the first in a series of curves C 1, C 2, C 3, etc., where C 1 is the pedal of C, C 2 is the pedal of C 1, and so on.