Let d be the n-th day of a year 2000+n, where n> - 248. Take the sum d + n + floor[(n + 3)/4] - floor[(n - 1)/100] + floor[((n - 1)/400] modulo 7. If the remainder is 0 then the day is Friday,
if the remainder is 1, then the day is Saturday, if the remainder is 2, then the day is Sunday, ..., if the reminder is 6, then the day is Thursday .
As an example for the date Feb. 29, 2020. Here d=60 (31 days of January and 29 days of February) and n=20. The sum is 60 + 20 + 5 - 0 +0 =85 which is congruent to 1 modulo 7 then the day is Saturday.
n is greater than - 248, because our calendars skipped 11 days in 1752. People living in Britain, America and other English colonies went to sleep on the night of Sept. 2, 1752, and when they woke up the next morning it was Sept. 14, 1752.
معرفة اليوم من التاريخ
كمثال، اذا كان التاريخ هو 1 يناير سنة 2030، فنجمع الأعداد
1 + 30 + 8
ثم نقسم المجموع على 7 فيكون الناتج 4 وعليه يكون اليوم هو الثلاثاء
As another example, the Independence Day of USA, July 4, 1776 was on Thursday. The sum according to the discussion above is: 186 + ( - 224 ) + ( - 56 ) - ( - 3 ) + ( - 1 ) which is congruent to 6 modulo 7.
This works for any year after the year 2000 except after the year 4000, if the year 4000 is a leap year.
I thought of this formula in 2000, but I couldn't get it. Two years later I obtained it.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Graphs