As a complete noob in mathematics, I was wondering, what is the simplest way to describe a (preferably 2-dimensional, becuase it will be simpler) non-euclidean space in mathematics.
For example in general relativity spacetime is a 4 dimensional non-euclidean space. And I am guessing it has some kind of a function that depends on the mass in it's surrounding and sort of curves the space accordingly.
But that is quite advanced stuff. What would be the simplest example, of a mathematical space as a function of some variable. (If I am making sense).
Note: I know upto basic calculus.
The study of spaces in this way sounds more like Topology. This has a lot to do with the fundamental definition of distance.
Many different types of spaces metric spaces are one powerful way of creating them.
Any function that meets the requirements can be stated to be a distance and give rise to different spaces of which some are equal.
The distance from x to y is the distance from y to x
The distance from x to y is greater than 0 and equal to 0 iff x = y
The distance from x to y plus the distance from y to z is greater than the distance from x to z.
anything that follows those rules gives a definition of distance and hence defines a space.
A simple example is the taxi cab metric where you can only "travel" on unit grids. so the distance between (a,b) and (c,d) = abs(a-c)+abs(b-d). Think about what a circle would look like in this space.
It looks like a diamond!