Persian Algorithmic Calendar

Ahmad Birashk proposed an alternative means of determining leap years for the Persian calendar. His technique avoids the need to determine the moment of the astronomical equinox, replacing it with a very complex leap year structure. Years are grouped into cycles which begin with four normal years after which every fourth subsequent year in the cycle is a leap year. Cycles are grouped into grand cycles of either 128 years (composed of cycles of 29, 33, 33, and 33 years) or 132 years, containing cycles of of 29, 33, 33, and 37 years. A great grand cycle is composed of 21 consecutive 128 year grand cycles and a final 132 grand cycle, for a total of 2820 years. The pattern of normal and leap years which began in 1925 will not repeat until the year 4745!

This is not the calendar in use in Iran! It is presented here solely because there are many computer implementations of the Persian calendar which use it (with which users may wish to compare results), and because its baroque complexity enthralls programmers like myself.

Each 2820 year great grand cycle contains 2137 normal years of 365 days and 683 leap years of 366 days, with the average year length over the great grand cycle of 365.24219852. So close is this to the actual solar tropical year of 365.24219878 days that this calendar accumulates an error of one day only every 3.8 million years. As a purely solar calendar, months are not synchronised with the phases of the Moon.