Limerick
(12+144+20 + 3 4**(1/2))/7 + 5*11 = 9**2 + 0
A dozen, a gross, and a score,
Plus three times the square root of four,
Divided by seven
Plus five times eleven
Is nine squared and naught a bit more.
I'm trying to relate this limerick to calendrics.
The first sum works out to 182, which is half a year.
Dividing by seven gives number of weeks in 1/2 year.
I'm not yet sure what to do about the rest. Anyway, thinking
about this has got me starting to think of a calendar related
item for as many integers as possible, along these lines:
2: days in a weekend
3: Maximum number of Friday the 13ths in a year.
4: quarters in a year
4: solstices and equinoxes in a year
4: number of principal phases of the moon
5: days in a work week
5: days at the end of the Egyption calendar and Mayan Haab not belonging to a month
6: Jubilees in 293 solar years
7: days in a week
8: years in an Octaetris
8: days in Roman market day cycle
8: leap days in 33-year cycle
9: weeks equal to 2 months and 2 days for April, June, August, October and December
10: days in the Egyptian and French Republican "week" (decade)
11: years after which Easter is ofter the same
11: leap weeks in 62-year cycle
11: leap years in Tabular Islamic 30-year cycle
11: usual annual epact increment (mod 30)
12: months in Julian/Gregorian calendar year
12: lunar months in a Islamic year
12: animals in the Chinese zodiac
13: months in calendar year with 28 day months
13: lunar months in a lunisolar long year
13: weeks in a quarter
14: days in two weeks (fortnight)
14: lunar months in a full moon cycle (approx)
14: different calendars in Julian, Gregorian, Hebrew calendars,
taking account of the days of the week
14: months in maximum period that one Friday 13th
comes after the previous Friday 13.
15: lunar months in a short yerm
15: years in Roman cycle of indication (tax collection)
15: leap days in 62-year cycle
16: full moon cycles in a Saros (approx)
17: lunar months in a full yerm
18: fumocies in 251 lunations (very close)
18: years in a Saros
19: years in a Metonic cycle
19: days in a Bahai month and Bahai months in a year
20: base of Mayan counting system
24: fumocies in 334 lunar months or 27 years
25: years of 365 days in an Egyptional lunar cycle of 309 months
26: weeks in half a year and fortnights in a whole year (approx)
27: years in 24 fumocies or 334 lunar months
28: years in a Julian cycle with days of week
28: days in month of 13 month calendar
28: days in February in a common year
29: days in February in a leap year
29: days in a short lunar month
30: days in a long lunar month
30: days in April, June, September or November
30: The number of years in a cycle of the Tabular Islamic Calendar
31: days in any other Gregorian or Julian month
33: years of 365 days plus 8 leap days have a mean length of 365.242424.. days
35: different possible dates for Easter (from March 22 to April 25)
38: eclipse seasons in a Saros
38: weeks in approximately 9 lunar months.
48: Number of Friday the 13ths in a 28-year Julian cycle
49: 364-day years in a Jubilee
49: lunar months reckoned to be 1447 days
52: weeks in a year (approx)
55: weeks in an abundant long lunisolar year
59: Usually, the number of days in two consecutive lunar calendar months
60: Base of the Babylonian counting system,
which survives in our minutes and seconds.
60: Years in Chinese calendar cycle based on 5 elements and 12 zodiac animals
61: eclipse seasons in an Inex
61: weeks in maximum period that one Friday 13th comes after the previous Friday 13.
62: years with 15 leap days has a whole number of weeks and of 5-day cycles.
The mean year is 365.241935... days.
64: lunar months close to 63 30-day months (see 703 for better approximation)
70: years for sidereal year to fall one day behind tropical year (approx)
71: leap weeks in 400 years for Gregorian mean year of 365.2425 days.
73: days in 1/5 year (approx)
73: days in 1/8 Venus synodic period (approx)
87: days that eight 12-month lunar years drift against eight solar years
91: days in a quarter (approx)
97: leap days in 400-year Gregorian cycle
97: weeks in appriximately 23 lunar months
99: lunar months in an Octaetris
103: years in a lunisolar calendar have
20 more abundant than deficient on average
110: short months in a Metonic cycle (approx, on average)
122: months in solar year of months 3 or 2 days long (see 241).
123: long years in 334-year cycle
125: long months in a Metonic cycle (approx, on average)
126: abundant less deficient years in 649-year cycle
128: years a Julian leap day is skipped would produce a mean year of
365.2421875 days
130: long years in 353-year cycle
135: lunar months in a Tritos and weeks in a week of weeks
153: days in 5 consecutive Julian/Gregorian months not containing February
161: months repeating 1 and 2 days per month for 161 months (241 days) form an accurate solar
calendar with a year boundary every 244 months.
183: 49-month cycles in 725 years
202: abundant less deficient years in 1040-year cycle
206: solar years about 209 years of 360 days
209: years of 360 days is close to 206 solar years
210: days in an Indonesian cycle of integer numbers of 5, 6, and 7-day cycles
223: lunar months in a Saros
223: lunar months in 16 fumocies
223: lunar months in 18 years
223: consecutive lunations is a very consistent period of time 6585.2653 .. 6585.3701 days
235: lunar months in a Metonic cycle
239: long years in 649-year cycle
241: days grouped alternately in months of 1 and 2 days (see 161) form an accurate solar calendar
241: days grouped in 3 day months for 80 months followed by a 2 day month form an accurate solar
calendar (new year every 122 months).
243: years in Venus transit rhythm
251: lunar months in 18 full moon cycles (approx)
258: centuries in a cycle of the precession of equinoxes (approx)
260: days in a Mayan Tzolkin
293: solar years in six jubilees
294: years of 364 days is very close to 293 solar years
309: lunar months in an egyptian 25-year cycle
334: lunar months in 27 years or 24 fumocies
334: years reckoned to be 4131 lunar months
353: years reckoned to be 4366 lunar months
353: days in a deficient short lunisolar year
354: days in a regular short lunisolar year
355: days in a abundant short lunisolar year
358: lunar months in an Inex
364: days in 52 weeks
365: days in a solar common year
365: days in a Egyptian calendar year, Mayan Haab cycle
366: days in a solar leap year
371: days in a leapweek year (53 weeks)
372: years in a Gregoriana reckoned to be 4601 lunar months
and also 784 eclipse seasons
383: long years in 1040-year cycle
383: days in a deficient long lunisolar year
384: days in a regular long lunisolar year
385: days in an abundant long lunisolar year (exactly 55 weeks)
391: years reckoned to be 403 lunar years
and also 824 eclipse seasons (Palmen cycle)
400: years in a Gregorian leap year cycle
409: lunar months in 33 years of 366 days (25 yerms)
412: days in a full moon cycle - fumocy (approx)
443: days in a short yerm
502: days in a full yerm
532: years in a Julian Easter cycle
584: days in a synodic period of Venus (approx)
649: years in shortest accurate lunisolar cycle (8027 months, 237042 days)
654: lunar months very close to 623 31-day months
688: Friday 13ths in a 400-year Gregorian cycle
703: lunar months very close to 692 30-day months
725: years in 183 49-month cycles
793: number of 1080ths of an hour that the mean Hebrew month
exceeds 29 days 12 hours.
850: lunar months in a 52-yerm cycle
896: years in the cycle of Bonavian Civil calendar (=7*128)
945: days in a week of weeks
945: days in 32 synodic months (approx)
945: days in 31 Gregorian months (frequently)
992: days that should have one lunisolar intercalary month
1004: days in 34 synodic months (approx)
1004: days in 33 Gregorian months (frequently)
1040: years in accurate lunisolar cycle (12863 months, 379852 days).
1447: days in a 49-month cycle (lunar)
1461: days in 4 Julian years including a leap year
1507: days should have 1 leap day to match Vernal Equinox year length
1508: days should have 1 leap day to match mean tropical year length
1689: years in a Goddess lunar calendar cycle (649-year cycle + 1040-year cycle)
2835: days in a Windu cycle of 96 lunar months (3*945)
2894: days (twice 1447) in 98 synodic months (approx),
also 7 full moon cycles (approx)
and 28 days short of 8 Julian years
2922: days in an Octaetris
3235: weeks in 62-year cycle
4131: lunar months in 334-year cycle
4366: lunar months in 353-year cycle
6300: years before New Eastern Orthodox calendar repeats (including week)
6585: days in Saros (approx)
6686: Martian days in a Martian 10-year cycle
6939: days in a Metonic cycle (approx)
6940: days in a Metonic cycle (approx)
7980: years in Julian day cycle (28x19x15)
8027: lunar months in 649-year cycle
9125: days in an egyptian lunar cycle of 25 years and of 309 lunar months
10227: days in 28-year Julian day of week cycle
10631: days in a Tabular Islamic 30-year cycle
12053: days in a 33-year cycle with 8 leap years
12863: lunar months in 1040-year cycle
17836: days in a Jubilee (49 364-day years)
18980: days in a Mayan calendar round
20871: weeks in a Gregorian 400-year cycle
22645: days in 62-year cycle
25101: days in a 52-yerm cycle
25920: months in which Hebrew molad repeats
27759: days in a Callypic 76-year cycle
107016: days in six jubilee cycle (294 364-day years)
121991: days in 334-year cycle (approx)
146097: days in a Gregorian 400-year cycle
237042: days in 649-year cycle
379852: days in 1040-year cycle
416385: weeks in Julian day cycle (7980 Julian years)
1872000: days in one cycle of Mayan long count
2914695: days in Julian day cycle (7980 Julian years)
etc.
The goal is to have something for as many numbers as possible.
If you'd like to add entries yourself, feel free to upload an
amended version of this file. -- Victor Engel
Added 334/27/24 relationship. Victor Engel 2003-01-27
I've added a few, and made some corrections. Victor Engel 2003-01-14
I've added many. Karl Palmen 2003-01-14
Additions paraphrased from Karl's email post of 2002-01-31
referencing Sepp's calendar numbers
Copyright by Contributors (alphabetized by last name):
Victor Engel
Jean Fontaine
Clarence Kelogg
Karl Palmen
Sepp Rothwangl
Amos Shapir
I've added more. Karl Palmen 2002-11-26