# 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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### Why is two variables enough to parametrize a surface?

For a surface S, how do we know that two variables is always enough to parametrize the surface? I am thinking that it has something to do with the number of directions you can move in. For parametric ...
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### How To Measure Work Done Against Friction On A Non-Linear Path?

I've been trying to solve how to find the Work done against friction as a ball rolls down a curve, but haven't been able to find anything matching what I want online. The solution I have came up with ...
91 views

### Parameterizing the parabola $9x^2 +y^2-6xy+4x-4y+1=0$

Find parametrization of curve given by equation: $$9x^2 +y^2-6xy+4x-4y+1=0$$ My attempt: Let's notice that \begin{split} 9x^2 +y^2-6xy+4x-4y+1=0 & \iff (3x)^2 -6xy + y^2 +4x -4y +1=0\\ & \...
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### What is meant by Hermann Weyl's proof by homogeneity of the bijective property of the affine parameterization of the time continuum?

This is a specific question I have regarding my broader question: How would Hermann Weyl's development of the time "continuum" be handled in contemporary mathematical language? I've ...
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### How would Hermann Weyl's development of the time "continuum" be handled in contemporary mathematical language?

The source of the quoted material is Space-Time-Matter by Hermann Weyl I started trying to summarized the following development of the mathematical treatment of parameterized time. Then I realized ...
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### Why is this composition of curve parametrisations a diffeomorphism?

In our class, we wrote the following: Connected curves (1-dimensional manifolds) can be parametrised globally; $\overrightarrow{\gamma}: I \subseteq \mathbb{R} \to \Gamma \subseteq \mathbb{R}^3$, ...
131 views

### How to convert a Cartesian Equation to Parametric Equation?

I'm trying to 3D plot the following cartesian equation in Blender 3.1: $$\left(x - x\left(\frac{z}a\right)\right)^2 + \left(y - y\left(\frac{z}a\right)\right)^2 = r^2$$ But in it's current Implicit ...
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