Month

:In Egyptian mythology, Month is an alternate spelling for Menthu.

Calendrical implications

Continued fractions of the decimal value for the synodic month quoted above give successive approximations for the average length of this month in terms of fractions of a day. So in the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed:

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: 29 days

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: 30

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: 59/2

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: 443/15

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: 502/17

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: 1447/49

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: 25101/850

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This is useful for designing purely lunar calendars, where months of 29 and 30 days (termed respectively hollow and full months) occur in some pattern that repeats after some number of months. A recently invented pure lunar calendar called the Yerm Calendar http://www.hermetic.ch/cal_stud/palmen/yerm1.htm makes use of all of the above approximations.

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More importantly, in lunisolar calendars, an integral number of synodic months is fitted into some integral number of years. The average length of the tropical year divided by the average length of the synodic month, i.e. the number of synodic months in a year, is (for epoch J2000):

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: 12.368266392

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Continued fractions of this decimal value give optimal approximations for this value. So in the list below, after the number of synodic months listed in the numerator, an integer number of tropical years as listed in the denominator have been completed:

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: 12

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: 25/2

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: 37/3

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: 99/8

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: 235/19 Metonic cycle

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: 4131/334

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The last three have actually been used in calendars.

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