True or false: every fourth year – each year divisible by four – is a leap year.
While you think about this, here is something else to consider. Suppose you really like the 2008 calendar that is now hanging on your fridge. After 2008 slides into the past, will you ever be able to use this favorite calendar again? In what future year will the days and dates of 2008 again line up properly?
You might start toward an answer by considering that a “common year,” as opposed to a “leap year,” is 365 days long, or 52 weeks plus 1 day. So, for example, if your birthday is on a Tuesday, let’s say, one year it will be on a Wednesday the next. That is, if neither year is a leap year.
If it weren’t for leap years, you could use your favorite calendar every seven years. But leap years mix up the way days and dates align year after year.
For example, you might continue toward an answer to the favorite-calendar question by reasoning that since a leap year has 366 days – 52 weeks plus 2 days – you would celebrate your Tuesday birthday on a Thursday the next year if either year were a leap year. But here you need to be careful because the extra day in a leap year is inconveniently added at the end of the second month of the year.
This recreation gets complicated pretty quickly, but for the fun of it you can use a most interesting on-line tool. This calendar calculator computes “identical years” – years in the past or future in which the days and dates line up the same as they do during any given year. You can use this tool to recycle a favorite old calendar you might have tucked away at the bottom of your kitchen junk drawer.
But for leap years like 2008 you don’t need a calendar calculator. Exactly 4 x 366 = 1464 days separate any given date in a leap year and the same date the next leap year. This is 209 weeks plus 1 day. Therefore, a leap-year calendar like 2008 will be good again after 7 leap years, or 28 calendar years.
So if you take good care of your 2008 calendar you can use it again in 2036, and again in 2064, and in 2092. Or, if you have a nice calendar from 1980, or 1952, or 1924, you can use it again this year.
But don’t get carried away until you answer the true-false question above.
Here’s the answer: false.
The set of rules and conventions that define our calendar include a rule for skipping leap years from time to time. Most of the time, every year that is cleanly divisible by 4 – like 2008 – is a leap year.
This would keep our calendar synchronized with the seasons if there were exactly 365 days plus 6 hours in a year. But actually, 1 year is 365 days 5 hours and 49 minutes long. If we added a leap day to our calendar every four years our calendar would slowly drift out of sync with the seasons.
So we skip leap years periodically; we skip three leap years every 400 years. The official rule is that century years are not leap years (even though they would be by the divisible-by-4 rule) unless the year is cleanly divisible by 400. With the leap-year-exception rule, year 2100 will not be a leap year, and our calendar will remain in sync with the seasons well into the predictable future.
Look for a new post on or about 9 March 2008.
