Here are some examples of triangles in Non-Euclidean Geometry... In Spherical Geometry, the sum of the angles of a triangle is always more than 180 degrees. Case in point, a "triangle" formed by the prime-meridian (0 deg longitude), from the equator to the north pole, the north pole to the equator along the 90 deg west longitude line, and the third side is along the equator back to the prime-meridian. All the angles in this triangle add up to 270 degrees! (90 + 90 + 90) Yes, all of the lines are straight lines in this geometry, what are know as geodesics or more commonly, great circle routes. In Hyperbolic Geometry the sum of the angles of a triangle could be more or less than 180 degrees due to the curvature of geodesics in that geometry. (Think of a saddle-shaped "plane"). For a case of less, think of the classical shape of the funnel that you see often representing a black hole in curved space-time. A triangle on that surface would have angles that add up to less than 180 degrees. Hope this helps you understand the strange worlds of Non-Euclidean Geometry. Paul L. Smith GIS Systems Analyst Hal-Tec Software Solutions, Inc.