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Questions tagged [parametrization]

For questions on parametrization, the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

Parametrization is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation. "To parameterize" by itself means "to express in terms of parameters".

Parametrization is a mathematical process consisting of expressing the state of a system, process or model as a function of some independent quantities called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrisation consists thus of one function of several real variables for each coordinate. The number of parameters is the number of degrees of freedom of the system.

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Reduce degree of freedom

Consider function $f: R^n \rightarrow R$ - function of n variables. The function is a black box, but I have a priori knowledge of $k$ functions $g_i: R^n \times R \rightarrow R^n$ - set of function $g_i(x, \alpha)$ such that $\forall x, \alpha: f(x)…
NovGosh
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Finding parametric representations fo the parts of the plane

How would I find parametric representations for the plane: $2x+3y+z=4$ for $0 \leq x + y + z \leq 7$ and $2 \leq x-y \leq 4$? I can do simple ones where only $x,y$ are restricted independently (forms a rectangle in the $x-y$ plane, but how would I…
Twenty-six colours
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Parameterizing this paraboloid for a triple integral

I am confused about how to find the bounds of integration for the following triple integral. I seem to have trouble figuring out how to parameterize these curves (like the paraboloid, below). Also, based on my parameterization, the function that I…
Gary
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Parameter wurdiynd

How would I parameterise this curve in 3D? I am confused since the diagrams deal with three variables in total – should I use complex numbers? I'm only used to two diagrams and haven't encountered a problem with three like this.
nomad609
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Parametrization of $3x^2+y^2-4z^2=1$, if $y=z^2-1$, $z\geq 0$

How to make a Trigonometric Parametrization of $3x^2+y^2-4z^2=1$, if $y=z^2-1$, $z\geq 0$. To find $\theta$ such that $r(\theta)=(\sqrt{3},2,\sqrt{2})$ Attempt Replacing the second equation on the first we arrived to $$3x^2+y^2-4y-4=1 $$ which is an…
Valent
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Find Parametrizations For The Lines In Which The Planes Intersect: X + Y + Z = 1, X + Y = 2

We need a point on the line of intersection. To get it, use the equations of the given planes as a system of linear equations. If we set z = 0 Can´t understand how x+y=2 and x+y= 1 when z = 0
JasperWT
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Parameterizing a non-centered circle

So basically I am stuck with parameterizing a curve. Half of a unit circle is centered at $(1,0)$ in the first quadrant and traced clockwise from $(0,0)$ to $(2,0)$. I am not so sure how to parameterize this.
F1ftys
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