clidean geometry, being used by astronomers, 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 and such with degrees, as for scientists, engineers, and mathematicians, radians are used to substitute degree measures. The size of a radian is determined by the requirement that there are 2pi radians in a circle. Thus 2pi radians equals 360 degrees. This means that 1 radian = 180/pi degrees, and 1 degree = pi/180 radians. See Appendix 1-3.In Euclidean Geometry, the simplest polygon is known as the triangle, containing three sides. There is no such thing as a two-sided polygon in Euclidean Geometry, as for Spherical Geometry, there is, being referred to as a lune, or biangle. See Appendix 1-4. A two-sided polygon is closely related to part of the moon that is commonly seemed. In lunes there are two noticeable things which should be noted. One, the two vertices do not lye on the poles of the sphere. Secon...
