Formula for the Day of the Week
Date: 05/21/97 at 11:08:07 From: Christine Durling Subject: Declaration of Independence Would you please tell us what day of the week the Declaration of Independence was signed on as well the formula to determine such? Thank you very much! Christine Durling, Education Media Specialist Bordentown Regional High School Bordentown, NJ 08505
Date: 05/27/97 at 14:53:12 From: Doctor Rob Subject: Re: Declaration of Independence This is a trick question, of course. The date at the top of the document is July 4th, 1776. I believe it was actually signed on July 2nd, however. Ignoring this historical technicality, the day of the week upon which July 4th, 1776, fell was Thursday. The rule is quite complicated. It goes like this: Let k be the day of the month. In this case, k = 4. Let m be the month, counting March as 1 and February as 12. (Here January and February are considered as the last months of the preceding year. This is to make Feb. 29th [if any] be the last day of the year. This also means that the values of C and D are those for the preceding year, so, for example, 1 Jan 2000 would have C = 19 and D = 99.) In this case, m = 5 (July). Let D be the last two digits of the year. In this case, D = 76. Let C be the first two digits of the year (the century). In this case, C = 17. For any real number x, let [x] be the greatest integer less than or equal to x, which you get by truncating any fractional part. Then compute: f = k + [(13*m-1)/5] + D + [D/4] + [C/4] - 2*C. Once you have this, then f - 7*[f/7] will give you the day of the week, with Sunday = 0, Monday = 1, and so on. In your case f = 4 + [64/5] + 76 + [76/4] + [17/4] - 34 = 4 + 12 + 76 + 19 + 4 - 34 = 81 and f - 7*[f/7] = 81 - 7*[81/7] = 81 - 7*11 = 81 - 77 = 4, or Thursday. This rule was given by a certain Rev. Zeller, and so is called Zeller's Rule. This works for the Gregorian calendar only. There is a simpler version for the Julian calendar. Recall that English- speaking countries used the Gregorian calendar beginning 14 Sep 1752, and before that used the Julian calendar. A good reference for calendar matters is the _Encyclopedia Britannica_, under the heading "Calendar". -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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