Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,427

Calendar

Does the website already have a calendar which gives the days for dates?
I had one page dedicated to this on my website.
I am reproducing the contents below. With graphics and better presentation, I guess this can be posted on the website homepage (hyperlink) if it does not already contain one.

What day of the week was August 13, 1968?
Tuesday

What day of the week was January 21, 1959?
Wednesday

What day was June 15, 1974?
Saturday

What day was October 2, 1869?
Saturday

What day of the week was August 15, 1947?
Friday.

What day would September 30, 2029 be?
Thursday

You would be able to answer such questions (for any century) within half a minute without referring to the calendar by learning the following steps:

(To understand the rationale of the computation, all the steps have to be read. However, for the calculation part of it alone, step No. 2 can be skipped).

1) Excess Days : (ED) :
The remainder obtained when a number is divided by 7.
e.g. ED of 10 is 3, ED of 215 is 5, ED of 365 is 1.
There are 365 days in a year and 366 days if it is a leap year.
Since ED of 365 is 1, if June 23, 1962 is a Saturday,
June 23, 1963 is Saturday + 1 = Sunday;
Similarly, since June 23, 1963 is a Sunday,
June 23, 1964 is Sunday + 2 = Tuesday (Since 1964 is a leap year).
A leap year is one in which the last two digits of the year is divisible by 4. E.g. In the year 1988, the last two digits are 88. Since 88 is divisible by 4, the year 1988 was a leap year.
When the year has last two digits as zeros, like 1800 or 1900, the year should be divisible by 400, only then it is a leap year.
e.g. Since 1900 is not divisible by 400, the year 1900 AD is not a leap year.

2) January 1, 0001 AD was a MONDAY.
For 100 years in the 1st century AD, ED = 100 since ED for one year is 1.
From 0001 AD to 100 AD, there were 24 leap years, since every fourth year is a leap year and 100 isnt divisible by 400, therefore, for 24 leap years, add ED of 24. (We have already reckoned ED for all the years as 1, hence, for the leap years were taking into account one additional ED).
100 + 24 = 124.
ED of 124 = 5.
Therefore, ED for the 1st century AD is 5.

The Second Century AD:
ED brought forward from the 1st Century:- 5
ED for 100 years = 100
ED for 24 leap years = 24
Total = 129
ED of 129 = 3
Therefore, ED for the second century AD is 3.

The Third Century AD:
ED brought forward from the 2nd Century : 3
ED for 100 years = 100
ED for 24 leap years = 24
Total = 127
ED of 127 = 1
Therefore, ED for the 3rd Century AD is 1.

The Fourth Century AD:
ED brought forward from the 3rd Century : 1
ED for 100 years = 100
ED for 25 years = 25
(because 400 AD was a leap year: 400 is divisible by 400)
Total = 126
ED of 126 = NIL
Therefore, ED of the 4th Century is NIL.

3) Central Factor :-
Central Factor (CF) is a combination of the Century factor and the year factor. From (2), it is inferred that ED for 400 years is NIL. The Central Factor (CF) is determined as given below:
Take the first two digits of the year. If the day for a date in the year 1969 is to be found, 19 in the case of 1969. Now, the resultant (19 in the above case) should be written in the form (4 x ) + A 19 can be written as 4 x 4 + 3 (x =4, A=3 ) Ignore x. From the table below, CF would be year 1.
Illustration :-To find the day August 13, 1968 is:- The first two digits of the year = 19, 19 can be written as 4x4 + 3; From the CF table below Therefore, CF for 1968 AD is 1.
Central Factor (CF) Table :-

Year of the form (4x) x 100  CF = year - 2
Year of the form (4x + 1) x 100  CF = year + 3
Year of the form (4x + 2) x 100 CF = year + 1
Year of the form (4x + 3) x 100 CF = year - 1 

4) Month Factor :-
Month Factor :

Month Month factor
January, October  NIL 
May  1 
August  2 
February, March, November  3 
June  4 
September, December  5 
April, July  6 

(5) ED Vs Day

Excess Days (ED)  Day of the week
NIL  Monday 
1  Tuesday 
2  Wednesday 
3  Thursday 
4  Friday 
5  Saturday 
6  Sunday 

6) To find the day:-
What day of the week was August 13, 1968?
( a ) CF = year 1 because 19 is of the form 4x + 3
Therefore, CF = 67
( b ) Number of leap years in the century : 17 (Every fourth year is a leap year, therefore, divide the last two digits of the year by 4, take the quotient alone, ignore the remainder; if the year is a leap year, but the date falls before February 29, deduct 1 from the number of leap years)
( c )Month Factor (MF) = 2
( d ) Date = 13
Total = 99
ED of 99 = 1
From the table ED Vs Day, it is seen that if the ED is 1, the day is Tuesday. Therefore, August 13, 1968 was a TUESDAY.

What day of the week was January 21, 1959?
CF = year 1 (since 19 = 4x +3)
i.e. CF = 59-1 = 58
No. of leap years = 14
MF = NIL
Date = 21
Add : 58 + 14 + NIL + 21 = 93
ED of 93 = 2,Therefore January 21, 1959 was a WEDNESDAY.
The Central Factor, the Month Factor and the ED Vs Day table have to be memorized. Further, during oral calculation, if the number to be added is 7 or its multiple, it can be ignored. In the above calculation, since 21 and 14 are multiples of 7, it would be enough to find the ED of 58 (ED of 58 = 2).
If you forget the month factor, the following method has to be adopted:
To find what day of the week September 15, 1969 was :
CF = year 1 = 69-1 = 68
No. of leap years = 17
Since the MF cannot be recollected, we would have to add the ED for all the days of each month till the month in which the day falls on, in this case September.
ED Jan = 3, ED Feb = NIL, ED Mar = 3, ED April = 2, ED May = 3, ED June = 2, ED July = 3, ED August = 3, Adding, we get 19. ED of 19 = 5.
Therefore, the Month Factor is 5!

Final Illustration :-
What day of the week was January 26, 2001? CF = year 2 = -1.
Leap years = NIL
MF = NIL
Date = 26.
Total = 25. ED of 25 = 4. Therefore, January 26, 2001 was a FRIDAY.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Calendar

This is what I have: Day of the Week you were Born.

A description page to go along with it would be really nice

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Enya_and_WeirdAl_fan

Member

Registered: 2019-12-26

Posts: 2

Re: Calendar

Hi.  i'm new to this forum.

While it is true that Spanish calendars list their weeks from Lunes to Domingo (Mondays to Sundays), in the United States and AFAIK, MOST places list their weeks from Sunday to Saturday.

I checked out your DayofWeek page and notice you list your weeks like the Spanish do.  Can you allow individual users to select their own preference for that?