General definition of parameter

[Ravik Rocha]

I'm reading a very general definition of parameter on this site Parameter definition - Math Insight.

I didn't understand why we call the variable $t$ of the curve $\alpha(t)=(\cos t,\sin t)$ a parameter.

For me $t$ in this case is a variable too according to the definition of the site I linked. If the definition of this site is right a parameter is either constant or change slower than the variable, which is not the case with this curve.

 

[Evgeny.Makarov]

Welcome to the forum!

I think the meaning of "parameter" is different in this context. This meaning is described in the article about parametrized curves.

 

[HallsofIvy]

In general we use the word "parameter" when we have an xy- coordinate system (in two dimensions) or and xyz- coordinate system (in three dimensions) but have the coordinates written in terms of some additional variables, other than x, y, and z.

"For me [FONT=MathJax_Math]t in this case is a variable too". Yes, t is a variable but that has nothing to do with whether it is a "parameter" or not. A parameter is always a variable.

Yes, the site you link to says "while parameters typically either don't change or change more slowly". That makes no sense to me even with the word "typically"! A common use of a "parameter" is in motion problems where the coordinates, x, y, and z, change as t, the time, changes. The case of a very slow moving an object is an example in which the parameter, t, changes much faster than the coordinates.

Don't believe everything you read on the internet!