# Question about parametrization and number of free variables

Hey guys, how come when you have a parametric equation with two free variables it creates a surface, but when you have a parametric equation with one free variable it draws out a line? I sort of get it intuitively, one dimension is just a line, two dimensions is a plane, so I guess this sort of corresponds to this effect, but is there a more rigorous explanation? I didn't know which section to put this in, sorry if it's not the right one.

HallsofIvy
Homework Helper
Hey guys, how come when you have a parametric equation with two free variables it creates a surface, but when you have a parametric equation with one free variable it draws out a line? I sort of get it intuitively, one dimension is just a line, two dimensions is a plane, so I guess this sort of corresponds to this effect, but is there a more rigorous explanation? I didn't know which section to put this in, sorry if it's not the right one.
That's pretty much it. A geometric set has "dimension n" means that we can determine specific points in the set using n free variables or parameters.

Bacle2