Investigation the Arithmetical or Tabular Islamic calendar

Abstract

Arithmetical calendar (or tabular calendar) is sometimes referred to as the Fātimid calendar but this is in fact one of several almost identical tabular Islamic calendars. This calendar introduced by Muslim astronomers in the 9th century CE to predict the approximate begin of the months in the Islamic lunar calendar. Chronologists adopted 11 leap years in a 30 year cycle. In the case of leap Hijri year they add one day to the last month of the Hijri year. The cycle of this calendar agree with the Smaller cycles (2–5.333 years) discovered by Galal and Rashed (2011) and coincide with the lag criterion given by Galal (1988).We suggested the Islamic tabular calendar. The Leap years of this suggested Islamic tabular calendar may be 2, 5, 7, 10, 13, 15, 18, 21, 23, 26 and 29. Our suggested Arithmetical calendar satisfies the mathematical patterns, while the old Arithmetical calendar (or tabular calendar) does not satisfy a known fixed rule.We conclude empirical formula for our suggested Islamic tabular calendar. From this empirical formula, we can calculate if the Hijric year after immigration is a leap or a non-leap year.