Today is February 29th, which is a day that is usually added to our calendar once every four years (on years that are multiples of 4, such as 2004, 2008, 2012, and 2016). This is to correct for the fact that the number of days it takes the Earth to completely revolve once around the sun is slightly more than 365.
I'd like to elaborate on that word usually though, as not every fourth year is a leap year.
Mathematically speaking, it's more accurate to say that a true solar year is closer to 365.25 days than 365 days, as each year is longer than 365 days by almost 6 hours. This is almost a quarter of a day unaccounted for, which justifies the inclusion of an extra day every fourth year (because by then, four quarter-days have accumulated, equaling a full day). Repeating the four-year sequence of "365 days, 365 days, 365 days, 366 days" would be perfect if a solar year was exactly 365.25 days.
It's not though. As a result, a few additional (and much rarer) nuances are included in our calendar, so that we maintain synchronization over several centuries. It turns out that one solar year is slightly less than 365.25 days, which means that the additional leap day every fourth year is a slight overcorrection that needs to be adjusted from time to time.
The generally accepted length of a solar year, based on observation and calculation, has been averaged to be 365.2425 days. This means that two additional calendar rules are implemented to keep our calendars consistent:
1. Our calendar removes a leap year once every one hundred years on the century-year (e.g., the years 1700, 1800, and 1900 were not leap years; they did not have February 29ths). Unfortunately, this readjustment goes a bit too far in counterbalancing this issue, which leads to...
2. Our calendar puts back the leap year in every century-year that's a multiple of 400 (e.g., the year 2000 and the year 2400 will have February 29ths, despite the years 2100, 2200, and 2300 not having them).
These two additional corrections to our calendar combine to remove 3 leap years every 400 years (called a "leap cycle"). This means that we have 97 leap years- not 100 leap years- every 400 years. Here's the math for a leap cycle:
97 leap years = 97 * 366 days = 35,502 days
303 common years = 303 * 365 days = 110,595 days
In a 400-year period: 35,502 + 110,595 = 146,097 days
146,097 days / 400 years = 365.2425, which is the precise average number of days we want to obtain for a solar year.
(It's those extra 97 leap days spread throughout the 400-day leap cycle that adds the ".2425" correction that we need, which is 97/400.)
Therefore, while individual leap years play an important part in the correction of our calendar, it's not until an entire 400-year leap cycle has completed that we're corrected to the accuracy and satisfaction of leading scientists and mathematicians.
Just a word of caution, however: "daily" still means "365 times per year" in most math or science contexts (especially in word problems and textbooks). It's never a bad thing to check with your teacher just to make sure, but you may want to reserve this fun math fact about leap year technicalities for dinner table conversations and social mixers.
If you'd like to listen to this leap year process explained by a fantastic astrophysicist with a dreamy voice, click here:
For more information on leap years, here's the Wikipedia article, which is a great start: https://en.wikipedia.org/wiki/Leap_year#Gregorian_calendar
Thank you for taking the time to read this blog post, and I hope everyone has a lovely Leap Day!