Apr 25, 2015 · 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.

Feb 15, 2011 · The point is that parametrization helped you solve a system of equations that would normally be very difficult or impossible to solve explicitly.

Feb 6, 2025 · Is there a rigorous definition of parametrization? From what I can see, there is no absolute definition of parametrization, but simply a set of ideals that try to come to as close as …

Jul 15, 2018 · Other answers are correct, shortest explanation: set x=0 in your equation to see the y intercept is sqrt (2), not 1.

Jul 20, 2015 · and this second parametrization is regular because its velocity anywhere is at least 1. So, my question is: given a non-regular parametrization of a curve, is there an algorithm to …

Oct 17, 2014 · A parametrization of a straight line from $P$ to $Q$ is $r (t)=tP + (1-t)Q$ as $t$ goes from $0$ to $1$. Four of these pieces with suitable start and stop values for $t$ will take …

Mar 22, 2021 · If it involves a more difficult curve, you need a parametrization of this curve or use some theorems about integrals over complex curves. Taking your specific example, you need …

Dec 5, 2023 · chart/parametrization are almost identical. I (as learnt from many books) use chart to mean a map (with the suitable conditions) going from the manifold to an open set in $\Bbb …

Arc length parametrization just means unit speed parametrization. The former is used for some dumb historical reasons, I think the latter is far clearer.

Jun 1, 2010 · The discussion focuses on the parameterization of a torus defined by the equations x (ø,ß)= (3+cos (ø))cos (ß), y (ø,ß)= (3+cos (ø))sin (ß), and z (ø,ß)=sin (ø) for 0≤ø,ß≤2π. The …