Number of Days in a Month
Date: 10/21/2000 at 21:10:00 From: Barbara Reyes Subject: Calendar Why can't all months of the year be the same number of days? In the information I find about calendars, the reason for the difference in the number of days is difficult for my 7- to 9-year-olds to understand. Please help me!
Date: 10/23/2000 at 11:59:17 From: Doctor TWE Subject: Re: Calendar Hi Barbara - thanks for writing to Dr. Math. As long as we're sticking with 12 months in a year, the months can't all be the same number of days because 365 isn't divisible by 12. So the months will average 30 5/12 days (ignoring leap years). That means that the best we could do is to have 5 months of 31 days and 7 months of 30 days. Leap years, of course, complicate this. Because the time it takes the Earth to rotate around the sun is not an even number of days (it's about 365.24 days), we have to add an extra day about once every 4 years to keep our calendar in sync with the seasons. Otherwise, over the course of about 750 years, summers and winters would do a complete reversal. For more information on leap years, type in "leap year" (without the quotes) and click on "that exact phrase" in our Ask Dr. Math search engine at: http://mathforum.org/mathgrepform.html Another complication deals with the human ego. July was named for Julius Caesar. Some accounts say that July was supposed to be a 30-day month, but when Julius Caesar adopted the calendar (called the Julian calendar because he introduced it to the Roman Empire), he did not want any other month being grander (i.e. longer) than the one named after him. So he took a day away from February (making it 29 days, 30 days on leap years) and added it to July, making July 31 days. Augustus Caesar (Julius Caesar's successor, for whom August was named) did not want his month to be inferior to Julius', so he took another day away from February (making it 28 days instead of 29) and added it to August to make it 31 to match July. That leaves us with a mess - 7 months of 31 days, 4 months of 30 days, and one month with either 28 or 29 days. For more information on calendars, check out the following websites: The Julian and the Gregorian Calendars - Peter Meyer http://www.hermetic.ch/cal_stud/cal_art.htm Calendar, A History - Timekeepers http://www.ernie.cummings.net/calendar.htm Calendars for Earth - Martian Time http://pweb.jps.net/~tgangale/mars/earthcal_new.htm Perhaps we'd be better off just starting a new calendar and making up our own. If we wanted months with all the same number of days (ignoring leap years), we'd have to make either 5 months of 73 days each or 73 months of 5 days each, because 5 and 73 are the only factors of 365. We could take the opposite approach and make all the months the same number of days on leap years, then "take away" a day on non-leap years. With 366 we have a few choices: 2 * 183, 3 * 122, or 6 * 61. Perhaps we could have 6 months of 61 days and take away one day on non-leap years. I realize I haven't made it any simpler, but perhaps explaining why our calendar is the way it is can help you to understand the complications. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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