# Calendar System

The Basis for our Calendar System

Because we are sensitive to light and dark, heat and cold (and our activities depend on these), we naturally divide time into units of light versus dark (days versus nights) and the cycle of warm and cold weather (years).  We also find it convenient to work with two shorter units: the week.  The week, as you know, consists of 7 days for reasons of history and tradition.  The month is the other unit, again for reasons of history and tradition, with lengths 28 through 31 days.

We have an odd assortment of days in a month for a reason.  Imagine that the year was exactly 360.000 days long.  With that nice round number, if we chose our "week" to be 3, 4,5, 6, or 12 days long and our "month" to be 24 or 30 days long, we would have a calendar in which every year started on at the beginning of a week and ended on the last day of a week. This is similar to every year beginning on a Sunday and ending on a Saturday.  We wouldn't have to worry if the (American) holiday July 4th falls on a Tuesday one year or a Saturday another year.  It would fall on the same day (and date of course) every year.  One calendar could be used forever, as a given date would always occur on the same day of the week, and no leap years would be needed.

However, we in fact, have 365.242199 days from one vernal equinox to the next -- the "tropical year".  This is used because it ties directly to the seasons.  That long number is obviously not an even number of days (so we need leap years), and it does not contain an even number of weeks.  So, a given day of the year or date in the year, falls on different days of the week in different years.

We deal with the fact that the year is not an even number of weeks by getting new calendars every year. Our calendar system, the Gregorian calendar system, adjusts for the fact that there are not an even number of days in a year by introducing leap years.  A leap year is a year in which we introduce one extra day – February 29 (there are normally only 28 days in February).

Leap Year Rule   Length of year if the rules are followed

Every year divisible by 4--------- 365.25

except those divisible by 100-----365.24

but with those divisible by 400--365.2425

except those divisible by 4000-365.24225

According to these rules, 1996 was a leap year, because it is divisible by 4 and not by 100.  The year 1900 was not a leap year, because it is divisible by 100 and not by 400.

1) As you may recall, the year 2000 is also a leap year.  Why?

Because it is divisible by 4.
Because it is divisible by 100.
Because it is divisible by 400.

The months, which no longer connect directly to the cycle of the moon's phases, are adjusted so that there are always just 12 months in a year, leap-year or not.