Golomb’s Answers: “Calendar Oddities” Solutions
December 8, 2010 |  by Solomon Golomb


1. These holidays have the same number for the day and the month: 1/1, 2/2, 5/5, 6/6, and 11/11.

2. These holidays have a fixed day of the week but not a fixed date: Monday, Tuesday, Sunday, Monday, Thursday.

3. For these holidays, the day of the month exceeds 12, so dates written, e.g. 3/17 or 17/3, are unambiguous even if one doesn’t know whether the American or European notation is being used.


Nodal, 27.21222 days long, determined relative to the node of the moon’s orbit.

Tropical, 27.32158 days long, determined relative to the equinox.

Sidereal, 27.32166 days long, determined relative to the fixed stars.

Anomalistic, 27.55455 days long, determined relative to perigee of the moon’s orbit.

Synodic, 29.53059 days long, relative to the sun (the time from one new moon to the next).

All these “lengths” are very long-term averages, since individual orbits of

the moon around the Earth vary considerably. The synodic month, from one new moon to the next, is the

basis for all major lunar (e.g., the Islamic) and luni-solar (e.g., the

Chinese and the Hebrew) calendars. The sidereal month is the time it takes for the moon to appear in the same position relative to the fixed stars, but by this time the Earth has moved forward, and it takes the moon 2.2+ additional days to catch up. Except for astronomers, few people pay attention to the other three “months.”


1. The dominical letter is one of the seven letters from A to G used to denote Sundays in a given year by the Church. The date of the first Sunday in January (1st for A, 2nd for B, etc.) determines the dominical letter for the entire year.

2. An ephemeris (Greek for “over a day”) is a daily listing of the positions of the sun, moon, and planets for a particular location on Earth.

3. To intercalate is to insert a “leap element” (e.g., a leap day in the Julian or Gregorian calendar, a leap month in the Chinese or Hebrew calendar) in a “leap year.”

4. The adjective bissextile means “relating to a leap year,” so named because the Romans inserted a second (“bis”) day to repeat the sixth (“sext”) day before the calends of March.

This “leap day” was later moved to February 29.

5. The calendrical meaning of an embolism is the unit of time (such as a leap day or leap month) inserted into a calendar to produce regularity. (I believe this meaning is older than the medical meaning of an unwanted insertion, such as a blood clot or air bubble, into a blood vessel.)


1. The Romans originally started their year with March, so September, October, November, and December were, at that time, the seventh, eighth, ninth, and 10th months, respectively. (Having the leap day in February thus was, originally, at the end of the year.) When January was made the first month, the old names stuck.

2. The Islamic year consists of 12 synodic lunar months, with no extra “leap months,” and 12 x 29.53059 (see part B. above) is 354.36708 days, nearly

11 days less than a solar year of 365.2425 days. (Here I’ve used the Gregorian calendar approximation to the solar year.)

3. In the Northern Hemisphere, the “summer solstice” is the longest day of the year, and would be the middle of summer if Earth’s climate responded instantly to the sun. However, the atmosphere, the oceans, and even the land masses act as temperature buffers, and it takes about half a “solar season” for the Earth’s temperature to respond.

4. Tsarist Russia remained on the Julian calendar until after the Bolshevik revolution, whereby dates were 13 days later than in the Gregorian calendar by that time. Thus the “October Revolution” occurred in Julian October, but in Gregorian November.

5. Just as the French Revolution replaced older systems of weights and measures with the metric system, they also introduced a new calendar, with names of months derived from weather and climate conditions. Thus Thermidor was a hot summer month. When the French Republican Calendar was abandoned in 1805, most people were happy to forget it, but the name “thermidor” survives in “lobster thermidor,” and is sometimes used by historians to refer to the time when a revolution loses its zeal.