The incredible accuracy of the Persian Calendar

from the series of short articles about calendars

The Persian Calendar is the most accurate solar calendar in the human history, following exactly the vernal equinoxes.
The years are grouped into cycles which begin with four normal years followed by a leap year, after which every fourth subsequent year in the cycle is a leap year (as in the Julian calendar). Cycles are grouped into grand cycles of either 128 years (composed of cycles of 29=5+4*6, 33=5+4*7, 33, and 33 years) or 132 years (composed of cycles of 29=5+4*6, 33=5+4*7, 33, and 37=5+4*8 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. Therefore, 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. This average is just 0.00000026 (2.6*10 to the '-7') of a day shorter than Newcomb's value for the mean tropical year of 365.24219879 days, an incredible accuracy.
The current cycle of 2820 years started on 15/3/1096 (New Style: 21/3/1096 AD).
Year numbering follows the Islamic chronology, Anno Hegira, with year 1 the year of Hegira (622 AD).

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