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Why does February have 28 days while the other months have 30 or 31?

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There was a time when the year began in the month containing the beginning of Spring, namely March. This meant that February was the last month of the year, and it originally had 30 days. (This is also why September, October, November, and December have roots for 7, 8, 9 and 10, respectively, even though they don't fall in those positions now.)

July and August were renamed for Caesars of Rome and at the time those months were only 30 days. To honor the greatness of the Caesars, those months were extended to 31 days each and the days were taken from the end of the year, which at the time was February.

When Christendom spread further, the beginning of the Calendar was changed to coincide with the month epiphany, rather than the pagan tradition of the month of the vernal equinox.
The months we have today came from the Romans; originally there were 10 months - which explains the September, October, November and December names - which come from the Latin for 7, 8, 9 and 10. The problems started when Julius Caesar became the dictator perpetuo (dictator for life). He wanted his own month (July) - all the months had to be shortened to create the new month.

Next, Augustus became emperor and he wanted his own month (August) and he also wanted it to be longer than July. To get August to be longer than July, poor February had to lose a couple of days.
Originally the calendar was used to track agricultural concerns and only had ten months March - December. the time that was to be January and February had no agricultural relevance. When the calendar was competed January continued with the numbering scheme after December and February simply ran out of days before March

It was a political, religious and superstitious decision made roughly 2700 years ago by the Roman King Numa Pompilius. Up to that point the Romans had a ten-month calendar with 304 days, and approximately 61 winter days (between December and March) that were not assigned to any month. Numa created a new twelve-month calendar with 355 days by adding January (29 days) and February (28 days). In general, February has contained 28 days ever since.
Interestingly, February's 28 days were the second month of the Roman civil calendar but the last (twelfth) month of their religious calendar.
This is quite involved and is concerned with pride and politics. This is a very simplified explanation.

Julius Caesar reformed the calendar because it was out of synchronisation with the actual seasons, this in the early part of 46BC. This year ended up by being 445 days long to bring the calendar back in line the the sky's and seasons.
Not surprisingly it was called the "year of confusion."

He created a calendar that more nearly matched the annual journey of the earth round the sun. There were twelve months with alternating lengths of 31 and 30 days.
The exception was February which had 29 days and Leap years gave February 30 days to keep the calendar correct. Much of his knowledge came from the Egyptians.
The senate had the month of Quintilius renamed July after Caesar as an honor to his reform.

When Augustus became emperor the senate voted that the month after, then called Sextilus, should be name in his honor and thus it became Augustus.
However the senate did not like the fact that Augustus's month had 30 days and Julius's has 31 so they changed Augustus to 31 days, taking the extra day from February. This threw into disarray the organized way the months changed from 30 and 31 days.

Not satisfied, they tinkered more altering the number of days in the months according to what they thought was important and because they did not want three consecutive months with 31 days.

Consequently February lost a day (except in leap years) and we were left with the apparently random way the months alternate.
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