Saturday, March 13, 2010

[rhrpkdug] Factor the calendar

PeriodDaysFactorization
Year3655 * 73
Leap Year3662 * 3 * 61
Julian Olympiad14613 * 487
Gregorian Cycle (400 years)1460973 * 3 * 3 * 7 * 773

Synodic month approximations

Mean month (days)Days in cycleFactorization
Chinese Taichu Calendar (old) 29 43/81 2392 2 * 2 * 2 * 13 * 23
Orthodox Easter computus 29 499/940 27759 3 * 19 * 487
Newton 29 26/49 1447 1447
Hebrew calendar molad 29 13753/25920 765433 131 * 5843
Hindu Surya calendar (modern) 29 7087771/13358334 394479457 394479457
Yerm Lunar calendar 29 451/850 25101 3 * 3 * 2789
Gregorian Easter computus 29 37405943/70499183 2081882250 2 * 3 * 3 * 3 * 3 * 5 * 5 * 5 * 7 * 19 * 773
Tibetan Phugpa calendar 29 3001/5656 167025 3 * 5 * 5 * 17 * 131
Dee Easter computus 29 864071/1628531 48091470 2 * 3 * 5 * 7 * 17 * 19 * 709
Hindu Arya calendar (old) 29 2362563/4452778 131493125 5 * 5 * 5 * 5 * 61 * 3449
Tabular Islamic calendar 29 191/360 10631 10631

Many values from Length of the Lunar Cycle.

The "Days in cycle" is the number of days for there to be an integer number of months. Multiply the mean month by the denominator.

The successor to the Taichu calendar used a non-constant model (cubic). The successor to that, the modern Chinese calendar, uses astronomical observations.

Noting that the Gregorian cycle (400 years) and the Hebrew calendar molad share no common factors, the Gregorian computus could be, and arguably should be, worse. Multiply the two periods to get a cycle of 111827465001 days.

The Metonic Cycle = 235 months = 5 * 47.

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