Great circle theorem and the application of the spherical cosine rule to estimate distances on a globe

Abstract

This research paper explores my interest in the Great Circle Theorem and Non-Euclidean Geometry to apply its theory in Earth Sciences and explore navigating flight distances across the globe. I use three different equations, based on the situation of the two points on the map and their relation with each other, to obtain approximate great circle distances between the two points. The values acquired from the final equation, which is derived from the Spherical Law of Cosines, is compared with the actual great circle distances between the two points on the globe. A percentage error is calculated and the average is found, after which a correlation is drawn between the percentage error and the magnitude of the value of the great circle distance.