In the first and second centuries BC, Greek thinkers took the Babylonian beginnings of astronomy, which included the zodiac, and incorporated their brilliant geometrical ideas to create a mathematical model of the heavens that was both useful and accurate. Ptolemy's Almagest (ca. 100-150 AD) marks the peak of the development of this Greek astronomy. This early astronomy viewed the heavens as a great rotating celestial sphere with a stationary Earth at its center. The stars were fixed to the celestial sphere, while the sun moved along the zodiac, making one full circle each year. We will survey some of the geometry used in developing coordinate systems on the celestial sphere and in projecting the sphere onto a plane to result in a working two-dimensional model of the heavens -- the astrolabe. In order to visualize this sphere-to-plane stereographic projection, we will work some basic computations with astrolabes that I will provide to the audience, and compare the 2D astrolabe to a 3D celestial globe.