What sophisticated field of mathematics provided the foundation for the astrolabe's calculations regarding celestial mechanics and coordinate conversion?
Answer
Spherical trigonometry
The astrolabe's capability to translate three-dimensional celestial positions into readable two-dimensional projections, and subsequently calculate relationships like local time or the direction of Mecca (the qibla), relied entirely on complex mathematical principles. Specifically, the underlying knowledge required for these conversions and calculations stems from spherical trigonometry. This branch of mathematics deals with the geometry of surfaces of spheres, which is precisely what is needed when dealing with the perceived motions and positions of stars and planets on the celestial sphere relative to an observer fixed on the spherical Earth.
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