I have read that there is a model of Euclidean Geometry in the Hyperbolic Plane, but can't find any description on the web in a digestible form and thought I'd ask this question: If one can describe the Euclidean Model of Geometry found in the Hyperbolic Plane in plain English, with math symbols here and there, but no need for formal proofs or anything at this point. I would just like to get an intuition of how it can be found in the Hyperbolic Plane.
To me this sounds like there is some way to create a model of say a cube or a sphere or something 2D like a rectangle or triangle, from the Hyperbolic Plane alone. It would be interesting to see an example of something 2D and/or 3D to help illuminate, but if it is too complicated then just a description of how you can apply the model would be a good start.
They say Hyperbolic Geometry is a non-Euclidean Geometry, but this would seem to mean that it is both non-Euclidean and yet capable of modeling Euclidean geometry, or something like that.
In addition to providing an explanation, please provide an example so I can see how it is applied.