“Non-Euclidean Geometry” the fields of geometry as applied to non-flat surfaces.

Euclid was an ancient mathematician who published a work called *The Elements*. This laid out the basic, common principles of geometry that we know today. However, Euclid only dealt with flat, two-dimensional surfaces.

When applying geometry to curved surfaces, many of Euclid’s principles don’t work anymore. There are at least two types of geometry – elliptic and hyperbolic – that are considered “Non-Euclidean.”

As an aphorism, “Non-Euclidian” might refer to something that’s confusing or convoluted, or that breaks from a common norm in such a way that the usual principles and rules don’t apply anymore.