# 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.

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### Linearly approximating coordinates on an N dimensional point from known positions in time.

Let's imagine an N dimensional point $P$. Let's assume that we know what $P$ looks like at time $t=0$ and $t=1$. Is there an elegant formula to find where $P$ is, assuming linear approximation, at any ...
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### Local Parametrizations cover unit $n$-sphere

Say I have a set $\mathbb{S}_n$ of $2^n$ vectors $s\in \mathbb{R}^{n+1}$ which are functions of $n$ parameters $\{ \theta_1,\theta_2,\ldots,\theta_n\}$. How can I prove that the set of all ...
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### Parameterization of a curve within a path integral?

I have a question about the following problem: Find an appropriate parametrization for the given piecewise-smooth curve in $\mathbb{R}^{2}$, with the implied orientation. The curve $C$, which goes ...
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### How to make a 2-d linear function using a third variable for the iterator? [closed]

Say, for example, you have the vector $\vec {PQ} = \langle8,4\rangle$. As we all learned in Algebra I, the "traditional" slope (y-units per x-unit) would be $\frac{4}{8}$, and the slope for ...
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### Parametric representation of the intersection of spheres

Goal: I am trying to find the curve of intersection of two spheres. \begin{align*}x^2+y^2+z^2 &= 9 \\ (x-3)^2+y^2+(z-1)^2 &= 4 \end{align*} What I have done: One of the ways of achieving ...
I can create a 3D Parametric Equation of a spiral but I'm having trouble getting the angle of "decent" to also change over time. $$x=u\sin(u)\cos(v)$$ $$y=u\cos(u)\cos(v)$$ $$z=-u\sin(v)$$ ...