A global Islamic calendar can be published by precalculating the presence of the Al-Hilal (the first visible crescent moon on earth).
From a historical angle, all of the events and celebrations of Islamic history are recorded in the Hijra Calendar
The Muslim calendar, based purely on lunar cycles, was first introduced by the second Caliph, `Umar ibn Al-Khattab using the event of Hijra
Fasting in the month of Ramadan is one of the five pillars that are obligatory requirements that a Muslim needs to fulfill