Perfect month
Perfect month
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A perfect month or a rectangular month designates a month whose number of days is divisible by the number of days in a week and whose first day corresponds to the first day of the week.[1][2] This causes the arrangement of the days of the month to resemble a rectangle. In the Gregorian calendar, this arrangement can only occur for the month of February.

Constraints

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To satisfy such an arrangement in the Gregorian calendar, the number of days in the month must be divisible by seven. Only the month of February of a common year can meet this constraint as the month has 28 days, a multiple of 7.[3]

For a February to be a perfect month, the month must start on the first day of the week (usually considered to be Sunday or Monday). For Sunday-first calendars, this means that the year must start on a Thursday, and for Monday-first calendars, the year must start on a Friday. It must also occur in a common year, as the phenomenon does not occur when February has 29 days.

Occurrence

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In the Gregorian calendar, the phenomenon occurs every six years or eleven years following a 6-11-11, 11-6-11, or an 11-11-6 sequence until the end of the 21st century. The most recent perfect months were February 2015 (Sunday-first) and February 2021 (Monday-first).[4] Due to calculation rules, the years 1700, 1800, and 1900 are not leap years, causing a shift in the sequence with two instances of three consecutive spacings of six years each (1693, 1699, 1705, 1711 and 1789, 1795, 1801, 1807) and a spacing of twelve years between 1891 and 1903 for Sunday-first calendars; or two consecutive spacings of six years each (1694, 1700, and 1706) and spacings of twelve years between 1790 and 1802, and 1897 and 1909 respectively for Monday-first calendars. The Gregorian calendar repeats every 400 years, so 2094, 2100, and 2106 will all feature perfect months with spacings of six years on Monday-first calendars; while 2093, 2099, 2105, and 2111 will all feature perfect months with spacings of six years on Sunday-first calendars.

The next perfect months will be February 2026 (Sunday-first) and February 2027 (Monday-first).

Attributes

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The calendar arrangement brings together notions of harmony and organization.[5][6]

See also

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References

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