Before we go to the answer just think about it that we have got 12 months to divide 365 days (except leap years). It gives us an average of 30.42 days in each month. So mathematicians should have decided to keep alternate months of 30 and 31 days to keep the calendar simpler. But sometime historical facts are not as simple as they seems to be. To get an answer to above questions you need to understand both history and mathematics of modern calendar.
History of Modern Calendar
The calendar that is being used worldwide today is Gregorian Calendar, which is made after doing some improvements in Julian Calendar. Julian Calendar was made from Traditional Roman Calendar.Roman Calendar was made by Romulus, the first king of Rome. March was the first month of that calendar named for a deity, Mars, known as an ancestor of the Roman people. Very few people notice the fact that word "Sept" is latin for 7, "Oct" for 8, "Nov" for 9 and "Dec" for 10. It means that September, October, November and December were 7th, 8th, 9th and 10th months respectively. At that time there were just 10 months in that calendar. Those months were Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December. At that time there were just 304 days in that calendar. 50 to 51 days after December were not named as it was the winter period which was not considered of any use.
Note: Quintilis and Sextilis are now known as July and August.
Julian Calendar was made using Roman Calendar and added months of Junarius and Februarius. In 44 BCE, the name of month Quintilis was changed to Julius to honor Julius Ceasar. In 4 BCE, month Sextilis was changed to Augustus to honor Emperor Augustus. Number of days are also increased from 29 to 31 in Augustus to honor him. This calendar had 355 days, which was still 10 days shorter than solar year. So after every few years a leap month was added between month of Feb and March, which was known as Mensis Intercalaris. Some historians believe that some kings and officials misused this month to extend their tenure in power.
Gregorian Calendar was introduced in 1582 by Pope Gregory XIII. Julian calendar was used to develop it after adjusting number of days in each month so that it can coordinate with solar year. Concept of leap year was also introduced in it and month of Mensis Intercalaris was removed, so that it can't be used for personal benefits by anybody.
Why do we add extra leap day in February ?
Due to historical facts and February being the last month added to the calendar, it was used to add leap day.Why February has got lowest number of days ?
There are two possible explanations for this. First explanation is that February was last month added to the calendar, hence got the lowest number of days. Second explanation is that earlier month of Februarius had 30 days and Sextilis had 29 days. But when Sextilis was named Augustus to honor Emperor Augustus, the number of days were increased to 31 by adding two days taken from Feb. Thus number of days in Feb reduced to 28.| Months (Roman) | Months (English) | Around 750 BC (Roman Calender) | Days before 45 BC | Days at present |
| Januarius | January | Not existed | 29 | 31 |
| Februarius | February | Not existed | 28 | 28, 29 |
| Mensis Intercalaris | Used as Leap Month | |||
| Martius | March | 31 | 31 | |
| Aprilis | April | 29 | 30 | |
| Maius | May | 31 | 31 | |
| Junius | June | 29 | 30 | |
| Quintilis (Julius) | July | 31 | 31 | |
| Sextilis (Augustus) | August | 29 | 31 | |
| September | September | 29 | 30 | |
| October | October | 31 | 31 | |
| November | November | 29 | 30 | |
| December | December | 29 | 31 | |
| Total Days | 304 | 355 | 365, 366 |
If you have got some additional facts regarding the information provided on this page then feel free to comment.
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