Date: Mon, 16 Mar 1998 20:20:23 EST Subject: The day of the week, July 24, 1837
My question: I think the level of the question is secondary. Thank you to anyone who can answer this question! Colleen (student) Hi Coleen The easiest way to find the day of the week is to consult a perpetual calendar; these can be found in reference books such as encyclopedias and almanacs. My Canadian World Almanac tells me that July 24, 1837 was a Monday. There is a formula for the day of the week, but it is complicated by the irregular month-length of our calendar, by the leap-year rule, and by the convention that the extra day in a leap year comes on February 29. To find the day of the week in the GREGORIAN (= our) calendar for day = d, in month = m, in year = y, IN THIS CENTURY OR THE NEXT (between March 1, 1900 and February 28, 2100), compute the numbers M and Y as follows. - We agree (because leap years have an extra day at the end of February) to let January and February be the be the 13th and 14th months of the year y - 1. Thus m runs from 3 (=March) to 14 (= Feb.). Define
M = 2m + [3(m+1)/5] - 1 (mod 7), where [3(m+1)/5] means the the whole number of times 5 goes into the product 3(m+1). If you don't like this formula, you can compute the 12 values of M once and for all:
m M 3 0 4 3 5 5 6 1 7 3 8 6 9 2 10 4 11 0 12 2 13 5 14 1 - Y = y' + [y'/4] where y' = y when m is a number from 3 to 12 and y' = y-1 for m = 13, 14. (As before, [y'/4] means the whole number of times 4 goes into y'.)
- The day of the week is d + M + Y (mod 7), where 0 means Monday, 1 means Tuesday, ... , 6 means Saturday.
subtract 1 for the 2100s, EXAMPLE: For July 24, 1837, d=24, m=7, and y=1837. M=3 and Y= 1837 + [1837/4] = 3 + 459 = 3 + 4 = 0 (mod 7). Remembering to add 1 for the 1800s, date = 24 + 3 + 0 + 1 = 0 (mod 7), so MONDAY.
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