A surface is defined as a 2-dimensional object that requires only two parameters to describe it, such as in the function f(x,y). While surfaces exist in 3-dimensional space, like the shell of a sphere, they remain fundamentally 2-dimensional. The third coordinate, such as the radius of the sphere, is not required to define points on the surface itself, emphasizing the distinction between surface dimensions and spatial dimensions.
PREREQUISITESStudents of mathematics, educators teaching geometry, and anyone interested in the principles of dimensionality in geometry and topology.
zezima1 said: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?