Teaching Mathematics and Scientificity: is an altitude of 1.5 km sufficient to show that the Earth is flat?

Abstract

The concept of a spherical planet Earth has been known since the time of the ancient Greeks, arround 2500 years ago (Crease, 2006). However, today, technological advances not only provide new ways to verify the Earth's sphericity but also amplify, through social media, the voices of denialist movements —including those claiming that the Earth is a flat disc covered by a dome containing the Moon and the Sun (Albuquerque & Quinan, 2019; Bertotti, 2020; Lewandowsky & Cook, 2020; Sousa Filho, 2020). This article presents a discussion aimed at supporting mathematics teachers in addressing this topic while exploring concepts from the History of Mathematics, geometry, trigonometry, proportion, and limits at the school level. We mathematically demonstrate that observations from low altitudes —such as the fatal experiment conducted by Mark Hughes in 2020 —are inconclusive regarding the Earth's sphericity. This analysis led us to develop simple expressions that allow us to compare distances on the surface (geodesic) with those through the solid Earth (as if traversed inside the globe), as well as to calculate the percentage of the Earth's surface visible to an observer located at a given height (H) above the ground.