<P> One can easily see how hyperbolic geometry breaks Playfair's axiom, Proclus' axiom (the parallelism, defined as non-intersection, is intransitive in an hyperbolic plane), the equidistance postulate (the points on one side of, and equidistant from, a given line do not form a line), and Pythagoras' theorem . A circle cannot have arbitrarily small curvature, so the three points property also fails . </P> <P> The sum of the angles can be arbitrarily small (but positive). For an ideal triangle, a generalization of hyperbolic triangles, this sum is equal to zero . </P> <P> For a spherical triangle, the sum of the angles is greater than 180 ° and can be up to 540 ° . Specifically, the sum of the angles is </P> <Dl> <Dd> 180 ° × (1 + 4f), </Dd> </Dl>

Sum of three angles of a triangle is 180 degrees