User:B. P. de la Calzada

Determining the day of the week of the Gregorian Calendar!

Day of the week maybe calculated (mentally)with simplicity using the method of Arthur Benjamin, Ph.D. and Michael Brant Shermer Ph.D. in their book "Mathemagics" with slight modification(bpc)

With a given date, a day of the week can be determined by calculating the formula; Wd = (Cn+Yn+Mc+D)-M7.

Where: Wd = the number representing Weekday (value 0-6; 0=Sunday,1=Monday, 2=Tuesday, 3=Wednesday, 4=Thursday, 5=Friday,6=Saturday).

Cn = the century number assigned for the first two digits of the year, (for the two digits divisible by 4, Cn = -2 like 16,20,24, etc; for two digits not divisible by 4 but nearer or adjacent to the former but less like 15,19,23. etc.,Cn=-1; for two digits adjacent and greater like 17,21,25, etc., Cn =+3; and for two digits farther like 18,22,26 Cn=+1)

Yn = is the integer of the last two digits of the year multiplied by 1-1/4); that is dropping any remainder.

Mc = month code from 'Mathemagics' by Arthur Benjamin, Ph.D. and Michael Brant Shermer Ph.D; Mc =1 for January, Mc = 4 for February, Mc = 4 for March, Mc = 0 for April, Mc = 2 for May = 2, Mc = 5 for June, Mc = 0 for July, Mc = 3 August, Mc = 6 for September, Mc = 1 for October, Mc = 4 for November, and Mc = 6 for December. For Leap years only January and February change to 0 and 3 respectively.

D = the date ( value is from 1-31) and M7 = is the highest multiple of 7. B. P. de la Calzada (talk) 10:20, 17 December 2013 (UTC)

Example:# 1 October 15, 1582

Procedure;

1. Check out the first two digit of the year, it is 15 not divisible by 4 but adjacent to 16 and is less, then Cn = -1

2. Get the last two digits of the year and multiply by 1 1/4 and drop any decimal places; 82 *1.25 = 102.5 use Yn = 102.

3. The month is October from the tables it is 1, Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mc =  1.

4. The date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D = 15.

5. The algebraic sum is. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S = 117

6. Subtracting The highest multiple of 7,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M7 = -112

Then Wd = 5, (Friday)

Example # 2 4th March 1789 is Wednesday US Preamble to the Bill of Rights.

1. Check out the first two digit of the year, it is 17 not divisible by 4 but adjacent to 16 and is more, then Cn = +3

2. Get the last two digits of the year and multiply by 1 1/4 and drop any decimal places; 89*1.25 = 111.25 use Yn = 111.

3. The month is March from the tables it is 4, Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mc =  4.

4. The date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D =  4.

5. The algebraic sum is. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S = 122

6. Subtracting The highest multiple of 7,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M7 = -119

Then Wd = 3, (Wednesday)

Example # 3 12th February 1809 is Sunday birth of US 16th Pres. Abraham Lincoln

1. Check out the first two digit of the year, it is 18 not divisible by 4 not adjacent to either 16 or 20,then Cn = +1

2. Get the last two digits of the year and multiply by 1 1/4 and drop any decimal places; 09*1.25 = 11.25 use Yn =  11.

3. The month is Feb not leap year from the tables it is 4, Use. . . . . . . . . . . . . . . . . . . . . . .  Mc =   4.

4. The date. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D = 12.

5. The algebraic sum is. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S =  28

6. Subtracting The highest multiple of 7,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M7 = -28

Then Wd = 0, (Sunday)