The Handy Math Answer Book

(Brent) #1
What was the Roman calendar?
The first Roman calendar, according to legend, appeared when Rome was founded
around 750 BCE. When it actually started is still up for discussion, but the calendar was
based on the complexity of the solar-lunar cycles. At first, the calendar had ten months,
starting in March; January and February were added as the calendar was modified. Poli-
tics entered into the determination of this calendar, too, with certain officials deciding
to add days whenever they desired, and even what to name certain months.

What was the Julian calendar?
By the time of Julius Caesar (100–44 BCE), Roman calendar-keeping was a mess. Cae-
sar decided to reform the Roman calendar, asking help from astronomer and mathe-
matician Sosigenes of Alexandria (lived c. 1 BCE; not to be confused with Sosigenes the
Peripatetic [c. 2nd century], an Egyptian philosopher). The year 46 BCEwould conse-
quently have 445 days—a time appropriately called “the year of confusion.”
Sosigenes began the reformed year on January 1, 45 BCE, a year with 365 days, and
proposed an additional day for every fourth year in February (leap day). The alternate
months of the year (January, March, May, July, September, November) had 31 days;
the other months would have 30 days. In the Julian Calendar, there was only one rule:
Every year divisible by four was a leap year.
The vain heir to Caesar, Augustus Caesar (63 BCE–14 CE; a.k.a. Gaius Octavius,
Octavian, Julius Caesar Octavianus, and Caesar Augustus), would change the Julian
calendar in a several ways. Not only did he name the month of August after himself,
but he would change the number of days in many months to their present usage,
adding more confusion to the calendar.
The Julian calendar would govern Caesar’s part of the world until 1582. Not that the
Julian year was perfect: A year’s 364.25 days was too long by 11 minutes 12 seconds.
Although the difference between today’s measurement of the year and the Julian year was
not great, it adds up to 7.8 days over 1,000 years. But as with many decrees and mandates,
Caesar, Sosigenes, and Octavian left it up to future generations to fix the problem.

What is the Gregorian calendar?
By 1582 the discrepancies in the Julian calendar were not interfering with timekeep-
ing, but they were beginning to infringe on dates of the church’s ecclesiastical holi-
days. The powerful Catholic church was not amused: Pope Gregory XIII, on the advice
of several of his astronomers, decided to reposition days, striking out the excess ten
days that had accumulated on the then-present-day calendar. Thus, October 4, 1582,
was followed by October 15, 1582.
To fix the extra-days problem, the pope made sure that the last year of each centu-
ry would be a leap year, but only when it is exactly divisible by 400. That means that
62 three leap years are suppressed every four centuries; for example, 1900 was not a leap

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