The Mathematics of the Astrolabe and Its History

In this article we trace the scientific and cultural history of the astrolabe, a mechanical instrument used in the past for astronomical measurements and navigational purposes. The story of the astrolabe is interesting from several points of view, since it intertwines mathematical developments, geographical explorations, changing worldviews, and different cultures and civilizations. In our explorations we move from the early understanding of the world due to the Greeks, to the loss of their work, its rediscovery, the reception of Arab thinkers in Western natural philosophy, and, finally, to the new European culture that emerged with the end of the Middle Ages and the beginning of the early Renaissance. We present a mathematical analysis of how the Celestial Sphere can be represented on the plane through the stereographic projection: this is the consequence of some geometrical results of Apollonius, together with later refinements, whose first traces appear in the work of Al-Farghani.