In Euclidean geometry, the "angle of parallelism" is a constant; that is, any distance formula_1 between parallel lines yields an angle of parallelism equal to 90°. In hyperbolic geometry, the angle of parallelism varies with the formula_2 function. This function, described by Nikolai Ivanovich Lobachevsky, produces a unique angle of parallelism for each distance formula_3. As the distance gets shorter, formula_2 approaches 90°, whereas with increasing distance formula_2 approaches 0°. Thus, as distances get smaller, the hyperbolic plane behaves more and more like Euclidean geometry. Indeed, on small scales compared to formula_6, where formula_7 is the (constant) Gaussian curvature of the plane, an observer would have a hard time determining whether he is in the Euclidean or the hyperbolic plane.