There is some controversy about the reference meridian at which the equinox is determined in this calendar. Various sources cite Tehran, Esfahan, and the central meridian of Iran Standard Time as that where the equinox is determined; in this implementation, the Iran Standard Time longitude is used, as it appears that this is the criterion used in Iran today.
As this calendar is proleptic for all years prior to C. 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 years composed of cycles of 29, 33, 33, and 33 years or years, containing cycles of of 29, 33, 33, and 37 years.
A great grand cycle is composed of 21 consecutive year grand cycles and a final grand cycle, for a total of years. The pattern of normal and leap years which began in will not repeat until the year ! 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 year great grand cycle contains normal years of days and leap years of days, with the average year length over the great grand cycle of So close is this to the actual solar tropical year of As a purely solar calendar, months are not synchronised with the phases of the Moon.
Haab: Tzolkin: The Mayans employed three calendars, all organised as hierarchies of cycles of days of various lengths. The Long Count was the principal calendar for historical purposes, the Haab was used as the civil calendar, while the Tzolkin was the religious calendar. All of the Mayan calendars are based on serial counting of days without means for synchronising the calendar to the Sun or Moon, although the Long Count and Haab calendars contain cycles of and days, respectively, which are roughly comparable to the solar year.
Based purely on counting days, the Long Count more closely resembles the Julian Day system and contemporary computer representations of date and time than other calendars devised in antiquity. Also distinctly modern in appearance is that days and cycles count from zero, not one as in most other calendars, which simplifies the computation of dates, and that numbers as opposed to names were used for all of the cycles.
The Long Count calendar is organised into the hierarchy of cycles shown at the right. Each of the cycles is composed of 20 of the next shorter cycle with the exception of the tun , which consists of 18 uinal of 20 days each. This results in a tun of days, which maintains approximate alignment with the solar year over modest intervals—the calendar comes undone from the Sun 5 days every tun. The Mayans believed at at the conclusion of each pictun cycle of about 7, years the universe is destroyed and re-created.
Those with apocalyptic inclinations will be relieved to observe that the present cycle will not end until Columbus Day, October 12, in the Gregorian calendar. Speaking of apocalyptic events, it's amusing to observe that the longest of the cycles in the Mayan calendar, alautun , about 63 million years, is comparable to the 65 million years since the impact which brought down the curtain on the dinosaurs—an impact which occurred near the Yucatan peninsula where, almost an alautun later, the Mayan civilisation flourished.
If the universe is going to be destroyed and the end of the current pictun , there's no point in writing dates using the longer cycles, so we dispense with them here. For civil purposes the Mayans used the Haab calendar in which the year was divided into 18 named periods of 20 days each, followed by five Uayeb days not considered part of any period. Dates in this calendar are written as a day number 0 to 19 for regular periods and 0 to 4 for the days of Uayeb followed by the name of the period.
This calendar has no concept of year numbers; it simply repeats at the end of the complete day cycle. Consequently, it is not possible, given a date in the Haab calendar, to determine the Long Count or year in other calendars. The day cycle provides better alignment with the solar year than the day tun of the Long Count but, lacking a leap year mechanism, the Haab calendar shifted one day with respect to the seasons about every four years.
The Mayan religion employed the Tzolkin calendar, composed of 20 named periods of 13 days. Unlike the Haab calendar, in which the day numbers increment until the end of the period, at which time the next period name is used and the day count reset to 0, the names and numbers in the Tzolkin calendar advance in parallel. On each successive day, the day number is incremented by 1, being reset to 0 upon reaching 13, and the next in the cycle of twenty names is affixed to it.
Since 13 does not evenly divide 20, there are thus a total of day number and period names before the calendar repeats. As with the Haab calendar, cycles are not counted and one cannot, therefore, convert a Tzolkin date into a unique date in other calendars.
The day cycle formed the basis for Mayan religious events and has no relation to the solar year or lunar month. The Mayans frequently specified dates using both the Haab and Tzolkin calendars; dates of this form repeat only every 52 solar years.
A bewildering variety of calendars have been and continue to be used in the Indian subcontinent. In the Indian government's Calendar Reform Committee adopted the National Calendar of India for civil purposes and, in addition, defined guidelines to standardise computation of the religious calendar, which is based on astronomical observations.
The civil calendar is used throughout India today for administrative purposes, but a variety of religious calendars remain in use.
We present the civil calendar here. The National Calendar of India is composed of 12 months. The first month, Caitra , is 30 days in normal and 31 days in leap years. This is followed by five consecutive 31 day months, then six 30 day months. Leap years in the Indian calendar occur in the same years as as in the Gregorian calendar; the two calendars thus have identical accuracy and remain synchronised.
Years in the Indian calendar are counted from the start of the Saka Era, the equinox of March 22nd of year 79 in the Gregorian calendar, designated day 1 of month Caitra of year 1 in the Saka Era.
Since year 1 of the Indian calendar differs from year 1 of the Gregorian, to determine whether a year in the Indian calendar is a leap year, add 78 to the year of the Saka era then apply the Gregorian calendar rule to the sum. In with the relentlessly rational! Months are grouped into four seasons; the three months of each season end with the same letters and rhyme with one another.
The calendar begins on Gregorian date September 22nd, , the September equinox and date of the founding of the First Republic. Subsequent years begin on the day in which the September equinox occurs as reckoned at the Paris meridian. Days begin at true solar midnight. Whether the sans-culottides period contains five or six days depends on the actual date of the equinox.
Consequently, there is no leap year rule per se : day years do not recur in a regular pattern but instead follow the dictates of astronomy. The Republican calendar is rare in that it has no concept of a seven day week.
Instead, each of these holidays commemorates an aspect of the republican spirit. Thus France, one of the first countries to adopt the Gregorian calendar in December , became the only country to subsequently abandon and then re-adopt it. The Julian year is, therefore, on average The calendar year was intended to approximate the tropical solar year. Although Greek astronomers had known, at least since Hipparchus, that the tropical year was a few minutes shorter than As a result, the calendar year gained about three days every four centuries compared to observed equinox times and the seasons.
This discrepancy was corrected by the Gregorian reform, introduced in The arrangements made in the calendar after the death of Caesar could not be implemented properly. The fact that Pontifeksler, who made arrangements in the calendar, made a leap year application in 3 years, caused confusion again. During the 40 years of application in this way, there has been 3 days of slippage. Roman Emperor Augustus, BC. In the 8th year, it corrected this shift by stopping the leap year application for 12 years.
He also changed the name of August to his own name, Augustus. In the regulations made; It was taken 1 day from February, and added to August, after July 31 and August took 30 days. In this way, February took 29 days in leap years and 28 days in other years. Julian Calendar, BC. It was used from the 46th to the 16th century.
Leap year practice was applied in Julian Calendar for the first time in history. As a result of a small difference in this calculation, a 1-day shift occurred approximately every years. Due to the confusion created by this shift, the Julian Calendar was abandoned in the 16th century and the Gregorian Calendar was adopted.
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