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Every four years, besides some certain years, we have a leap year, where a 29th day is added to February in the Gregorian calendar, making the year 366 days long, rather than 365. This is to make up for the fact that a true astronomical year is not exactly 365 days.

My question is, why is February 29th the leap day? Is there any specific event or special occasion that occurred on February 29th?

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    Some sources say the leap day is February 24th. – kasperd Dec 26 '15 at 10:23
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The ancient Romans used to have the new year at the end of February. To fit the lunar and solar calendars, an extra month was sometimes added after February. This practice continued even after the months were shifted so that new year moved to where it is now (this shift is the reason why we have e.g. "december" 'tenth month', as number twelve). This proved to be problematic, as it was the Pontifex maximus who decided when to add this extra month, which was sometimes forgotten, or done/not done to gain political advantage. With the Julian reform, the months got the length we are used to, and the leap days as we know them were added.

See wikipedia on February for a somewhat longer history.

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The Wikipedia reference on February omits quite a bit of information. Simply put, the Roman religious year ended on 23 February (a.d. VII Kal. Mart. in the Roman counting backward and inclusively way...i.e., the 7th [6th in our counting] day before the first of March), with the Feast of Terminalia. (Before the Julian calendar, if they inserted an Intercalary month, February was in fact cut short at 23 days and the extra month then inserted between February and March.) Thus, when the Julian calendar was introduced, the natural place to insert a day was right after that. So in leap years, instead of the 24th day of February being a.d. VI Kal. Mart., the 25th day of February was a.d. VI Kal. Mart. and the 24th day was Bis a.d. VI Kal. Mart. (the second sixth day from the Kalends of March....of course, it precedes the first sixth day before since we are counting backward). Note "second sixth" hence the alternate name for leap year: "bissextile year".

In the Middle Ages, they kept the Roman numbering of days, so what we now call the 24th of February really was the leap day. Even after modern day-of-month notation came into vogue, the Catholic Church kept feast days that were on 24-28 February in normal years shifted by one day to 25-29 February in leap years, and this was not generally changed until 1970.

Note that saying Terminalia was the last day of the Roman sacred year does not mean that the next day was the first day of the new year. The sacred new year really did start on March 1 (as opposed to the political new year which had been January 1 since the mid-2nd century BC). But the last 5 days of February were the precursor to the new year celebration, and not part of the previous year. That's why intercalary months cut February short by 5 days (and then the entire intercalary month was a run-up to the new year with the festivals that precede the new year being celebrated on its last five days).

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