The astrolabe is a mechanical instrument to solve problems related to the position of sun and stars, in the past, at the moment and in the future. For example, you can determine when the sun rises on your birthday, or at what time the sun goes down. The astrolabe tells you how high the sun is in the sky at 11:00 on December 30. You can also determine what time it is when the star Betelgeuse in the constellation Orion is just above the horizon. With Islamic astrolabes you can determine the times of prayer. You can even find the direction of prayer towards Mecca.
The astrolabe is an old instrument. In Greek times, mathematical knowledge was available before the beginning of the era. The first descriptions date from the sixth century after the era. In the Arabic language area it is written about in the tenth century, for example by Abu Rayhan Muhammad ibn Ahmad al-Biruni. In museums there are copies from that same time. Four centuries later the first astrolabes appear in Western Europe.
Today, the astrolabe is a historical instrument and a great tool for understanding the mathematics behind the stereographic projection and spherical triangle measurement.
Below is an animation of an astrolabe with which you see step by step how the stereographic projection works and how all those different lines are geometrically constructed.
Links to other websites
Links to animation in Geogebra
Below are two images of the animation with Geogebra. It includes a stepwise explanation how all lines, circles and curves can be drawn. The animation can be configured for every time zone and latitude.