The Zigzag Function
This animation illustrates the zigzag function used in ancient Babylonian astronomy to predict the conjunctions of the Moon and the Sun (i.e. synodic periods in a lunisolar calendar). The data is sourced from The Exact Sciences in Antiquity by O. Neugebauer who in turn deciphered them from cuneiform tablets dated 133-132 BC.
The left hand graphics illustrates the motion of the Sun and the Moon. While the Sun moves through an arc of around 28/29 degrees on its orbits, the Moon should be understood to complete one revolution around the Earth and some more before the next conjunction.
The right hand graph plots the extent of the Sun's movement between two conjunctions. This increases / decreases by 0.3 degrees (18 arc minutes) between successive conjunctions.