How to determine the day of the week (DOW)

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HOW TO DETERMINE THE DAY OF THE WEEK (DOW)©

ARISTEO CANLAS FERNANDO
Peace Crusader and Echo

Most of us, most likely, use a calendar table to determine the day of the week (DOW) in the Gregorian calendar.  Fair and simple.  However, in the absence of such calendar table, how can we determine the DOW of today’s date, 2009-08-23, for example?

I would like to share with you my way without using any calendar table, just calculating mentally.  It is not for any century or any year of the Gregorian calendar.  The constant is the number of blank spaces before the first of the month from and including Monday, for the current month only because this is what affects me most.  For August 2009, the first of the month falls on a Saturday.  Therefore, there are five blank spaces before the first, which is the contant for the month.  This is for calendars in which Monday is the first column of the week or the week starts on Monday, like in Europe, which follows the ISO Week Date.  In the USA, I think it is Sunday.  Here in Australia, it is mixed — either Sunday or Monday.  Nothing is official yet with regards to this.

The constant to use this August 2009 is 5.  Here are the steps:

  1.  Add the constant for the month to the date.  (5 + 23 = 28)
  2. Divide the sum by 7.  (28/7 = 4 remainder 0)
  3. The remainder determines the DOW.  If it is 0, it is Sunday; 1, Monday; 2, Tuesday; 3, Wednesday; 4, Thursday; 5, Friday; 6, Saturday.

Another way to do this:

  1. Divide the date by 7.  (23/7 = 3 remainder 2)
  2. Add the constant for the month to the remainder to get the sum.  (5 +2 = 7)
  3. The sum determines the DOW.  If it is 1 or 8, it is Monday; 2 or 9, Tuesday; 3 or 10, Wednesday; 4 or 11, Thursday; 5 or 12, Friday; 6 or 13, Saturday; 7, Sunday.
  4. In Step 3, if the sum is 7 or more, subtract 7 from the sum to get the difference.  (e.g., 10 – 7 = 3)   The difference then determines the DOW.   Like in the preceding way, if it is 0, then it is Sunday; 1, Monday; 2, Tuesday; 3, Wednesday; 4, Thursday; 5, Friday; 6, Saturday.

Corresponding months are months that start the month on the same day of the week.  During common years, in the Gregorian calendar, they are:

January and October
February, March and November
April and July
September and December
No months correspond to May, June and August

Corresponding months during leap years in the Gregorian calendar are:

January, April and July
February and August
March and November
September and December
No months correspond to May, June and October

The constants for 2001 to 2020 in the Gregorian calendar are:

 

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

2001

0

3

3

6

1

4

6

2

5

0

3

5

2002

1

4

4

0

2

5

0

3

6

1

4

6

2003

2

5

5

1

3

6

1

4

0

2

5

0

2004

3

6

0

3

5

1

3

6

2

4

0

2

2005

5

1

1

4

6

2

4

0

3

5

1

3

2006

6

2

2

5

0

3

5

1

4

6

2

4

2007

0

3

3

6

1

4

6

2

5

0

3

5

2008

1

4

5

1

3

6

1

4

0

2

5

0

2009

3

6

6

2

4

0

2

5

1

3

6

1

2010

4

0

0

3

5

1

3

6

2

4

0

2

2011

5

1

1

4

6

2

4

0

3

5

1

3

2012

6

2

3

6

1

4

6

2

5

0

3

5

2013

1

4

4

0

2

5

0

3

6

1

4

6

2014

2

5

5

1

3

6

1

4

0

2

5

0

2015

3

6

6

2

4

0

2

5

1

3

6

1

2016

4

0

1

4

6

2

4

0

3

5

1

3

2017

6

2

2

5

0

3

5

1

4

6

2

4

2018

0

3

3

6

1

4

6

2

5

0

3

5

2019

1

4

4

0

2

5

0

3

6

1

4

6

2020

2

5

6

2

4

0

2

5

1

3

6

1

 

The Gregorian calendar is not perpetual, hence, we have to know the constant to use for each month of a year. 

In the Aristean calendar, there are only three constants – 0, 3, 5 – for the first, second, and third months of the quarter of any year.  They exclude, of course, December 31 (World Peace Day) and June 31 (Leap Year Day every four years) which are no-weekdays.

First month of the quarter (January, April, July, October) – 0
Second month of the quarter (February, May, August, November) – 3
Third month of the quarter (March, June, September, December) – 5

And we follow the first of the above three steps.

I also have the reverse of determining the date given the day of the week. 

Details are in http://www.geocities.com/peacecrusader888/calendaridx.htm.

Let us get used to 0 as Sunday, 1 as Monday, 2 as Tuesday, etc.  Later, we will be “using a  simpler, common, and universal calendar” which is perpetual.

File:  032-dow.htm     http://www.geocities.com/peacecrusader888/032-dow.htm
First uploaded:  2009-08-24     Last updated:  2009-08-24     Rev. No. 0

Copyright © 2009 Aristeo Canlas Fernando
All rights reserved.

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