Geometry

7 Pages 1671 Words

tronomers, pilots, and ship captains. In Euclidean geometry it is stated that the sum of the angles in a triangle are equal to 180. As for Spherical geometry it is stated that the sum of the angles in a triangle are always greater than 180. When most people try and visualize a triangle containing angle sums greater than 180 they say it’s impossible. They’re right, in Euclidean geometry it is impossible, but as for Spherical geometry, it is possible. Think of the triangle on a sphere, and then try and visualize it. See Appendix 1-1. When thinking of the Non-Euclidean Spherical Geometry, we start of with a basic sphere. A sphere is a set of points in three-dimensional space equidistant from a point called the center of the sphere. The distance from the center to the points on the sphere is called the radius. See Appendix 1-2 to visualize tangents, lines, and centers between the sphere, lines, and planes. Unlike standard Euclidean Geometry, in Spherical Geometry, radians are used to replace degree measures. It is usual for most people to measure angles an...