Can you briefly explain hyperbolic geometry for the layman?

Imagine making a quilt, but instead of sewing four squares to each corner, you have to sew five squares to each corner. The quilt cannot lie flat because there's too much material. This is just a crude approximation. read more

Imagine making a quilt, but instead of sewing four squares to each corner, you have to sew five squares to each corner. The quilt cannot lie flat because there's too much material. read more

And no, its not that I didn't like your rephrasing, I was just trying to express the idea of a hyperbolic curvature associated with a geometry other than just by coordinates, i.e., the metric, in agreement with what you said. read more