Apr 25, 2015 · This parameterization looks qualitatively different from the trigonometric parameterization $\gamma (t)$ above, but they are related by a clever and important change of variable related to …

Space filling curves are continuous, but wildly non-differentiable. There are a number of different definitions of "dimension" but for the one you're seeing in calculus, the functions have to be …

Aug 2, 2018 · What is the difference between parameterization and change of variables? How do I know when I'm doing one or the other? Also, under which one of these does "transformations" and …

Parameterization is necessary to capture what your curve actually is but the particular parameterization used doesn't matter. If you setup the same line integral with two different parameterizations, those …

Oct 17, 2014 · What is the appropriate parametric equation of the boundary of a square? For example, the unit circle has a parametric equation $x(t)=\\cos(t)$ and $y(t)=\\sin(t)$.

One of the conditions that sub-manifolds have to fulfill is to be the image of a map with a constant rank derivation (equal to the dimension of the domain). Hence having a regular curve, by knowing the …

Feb 27, 2016 · Two points aren't enough to specify a parabola. There are infinitely many parabolas that pass through those two points. To pin down which one you mean, we'd need a third point, too.

Feb 20, 2017 · How to find parameterization if 2 points are given? Ask Question Asked 8 years, 9 months ago Modified 8 years, 9 months ago

Aug 26, 2015 · According to Elementary Differential Geometry by A N Pressley, a parameterization for Mobius strip is : $\\textit{Example 4.9}$ The Möbius band is the surface obtained by rotating a straight...

The answer to your question will depend on what you want to do with the ellipsoid. The Wikipedia page on geodesics on ellipsoids gives three possible parametrizations of the surface: (1) geographic …