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January 23, 2012
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March 1, 2012

Leap Year

If you’re having trouble keeping up with your homework, I have some good news for you: You get an extra day this year.

2012 is a leap year. That means that February has 29 days this year. That happens every four years (well, almost, see below). Ever wonder why our calendar can’t seem to make up its mind? The problem is that when you try to make a calendar year work out evenly with a solar year, you get a remainder (sound familiar math students?). A calendar year has 365 days, but it actually takes 365 ¼ days for the earth to orbit the sun. Not much of a problem when you are just counting sunsets and sunrises, but when you try to nail it down to a calendar with the same number of days each year, you run into problems after a few years. Without the leap-year adjustment, we would get behind by one day every four years. Within a century, we’d be off by almost a month.

Screen shot 2012-02-24 at 12.04.32 PM

So the obvious solution is to just add a day every four years. The Egyptians came up with the plan a long time ago. When the Romans took up the idea, they decided that February would be the month to get the extra day. So that’s why we have an extra day in February every four years. Almost.

The leap-day plan didn’t quite take care of everything because a solar year is actually a little less than 365 ¼ days. Eleven minutes, 14 seconds less, to be exact. If it takes an entire four years to get off by a day, why bother with eleven minutes, more or less? But even being off by only eleven minutes, we would still gain a day every 128 years. And that could get messy eventually. So we make another adjustment. We don’t add leap days to century years (1600, 1700, 1800, and so on) unless they are evenly divisible by 400. This pretty much takes care of the problem. The calendar year and the solar year are still off by about half a minute, but it will take 3300 years for the calendar year and the solar year to get off by a whole day. I think we’ve got it covered for now.

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