Talk:First fundamental form

Flawed example

The example is flawed: 1) the parameterization does not cover the entire unit sphere, and 2) it is not 1-1 on the given domain. The point (u,0) is mapped to the point (0,0,1) regardless of u.

It should state that a parameterization of the unit sphere minus two poles is given by ... with the domain of v as (0,pi) — Preceding unsigned comment added by 155.148.10.79 (talk) 15:52, 5 February 2008 (UTC)

I would add that the curve is not on the unit sphere, taking the point (u,v)=(pi/2,0) which is part of the domain maps to the origin

Incorrect evaluation

The "Length of a Curve on a Sphere" section incorrectly evaluates ${\sqrt {\sin ^{2}{t}}}$ as $\sin {t}$ instead of the correct $|\sin {t}|$. — Preceding unsigned comment added by 129.237.129.169 (talk) 21:02, 29 March 2013 (UTC)

Why a "spherical curve" in the example?

The example currently reads: "For a spherical curve on the unit sphere in R³ may be parametrized as". I find this to be weirdly worded. Why a "spherical curve"? As far as I can tell, the given parametrisation is for a sphere, not a curve on a sphere. Luca (talk) 09:24, 18 July 2021 (UTC)