A trigonometria no triângulo inscrito na superfície esférica: uma abordagem de sua aplicabilidade em determinar rotas de voos dos aviões

Abstract

This work investigates, from a theoretical perspective, the use of spherical trigonometry to calculate distances between points on the Earth’s surface, with direct application in aviation. The research begins with the foundations of spherical geometry, highlighting its emergence from Euclidean geometry, especially in light of the questions raised by Euclid’s fifth postulate. The central proposal is to analyze how the spherical triangle can represent air routes with greater precision. To this end, real geographic coordinates of Brazilian airports were used to calculate the orthodromic distance between these two points on the sphere. The results show that methods based on spherical geometry offer more accurate measurements compared to those based on plane geometry, especially on long-haul routes used by commercial aircraft. It is concluded that spherical trigonometry is an essential tool for air navigation, significantly contributing to efficient route planning. Furthermore, the work reinforces the importance of understanding the historical and theoretical foundations of non-Euclidean geometry, highlighting its role in applications that require mathematical rigor with the physical reality of the planet.