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?
A 2-dimensional world refers to a space that has only two dimensions - length and width. This means that objects in a 2-dimensional world have no depth or thickness, and can only be described using two coordinates.
As humans, we perceive a 2-dimensional world by projecting it onto a flat surface, such as a piece of paper or a computer screen. Our brains then interpret this projection and create the illusion of depth and dimension.
Some examples of 2-dimensional objects include shapes, such as circles, squares, and triangles, as well as images, like photographs and paintings. Maps are also considered 2-dimensional representations of our 3-dimensional world.
Understanding surface dimensions is crucial in many fields of science, such as physics, mathematics, and computer science. In physics, the concept of 2-dimensional surfaces is important in studying the behavior of waves and particles. In mathematics, the study of geometry and topology heavily relies on understanding and visualizing 2-dimensional objects. In computer science, 2-dimensional representations are used in creating graphics and animations.
Yes, there can be more than 2 dimensions in a surface. In fact, surfaces can have any number of dimensions, depending on the context and the definition used. For example, a 3-dimensional cube can be represented as a 2-dimensional surface using projection, and a 4-dimensional hypercube can be represented as a 3-dimensional surface. However, in the context of understanding surface dimensions, we typically refer to a surface with only two dimensions.