What Makes a Surface 2-Dimensional?

[zezima1]

What is the dimension of a surface? My book says it's only 2-dimensional and I guess that makes sense because you only need two parameters to describe it. But other than that it's not really intuitive for me. I mean surely the shell of a sphere can't be vizualized in a xy-coordinate system only?

 

[HmBe]

It's a 2 dimensional object in 3 dimensional space. You can have a function f(x,y) which will give you surface, and obviously only has 2 variables, or dimensions.

 

[DaveC426913]

What is the dimension of a surface? My book says it's only 2-dimensional and I guess that makes sense because you only need two parameters to describe it. But other than that it's not really intuitive for me. I mean surely the shell of a sphere can't be vizualized in a xy-coordinate system only?

As soon as you say the surface is on a sphere, you are invoking a third coordinate. The radius of the sphere will uniquely define the point in 3D space.

But it is not necessary to use this coordinate when defining a point on the surface of the sphere.