Monday’s Child

November 24, 2014 at 8:25 pm Leave a comment

Lyrics

Monday’s child is fair of face,
Tuesday’s child is full of grace,
Wednesday’s child is full of woe,
Thursday’s child has far to go.
Friday’s child is loving and giving,
Saturday’s child works hard for a living,
But the child born on the Sabbath Day,
Is fair and wise and good in every way.

Day of the Week Calculator

Day of the Week you were Born – Math is Fun

Zeller’s Algorithm: Day of the Week

Suppose we know the date as month, day and year. What day of the week do we have? One way to do this is a technique developed by Dr. Christian Zeller, a 19th Century German scholar.

The algorithm itself

The algorithm uses a number of variables, all type Integer.

Suppose we have Month (1-12), Day (1-31) and Year.

Now:

If Month is 1 or 2 Then
A = Month+10
NewYear = Year – 1
Else
A = Month-2
NewYear = Year
End If

B = Day

C = which year of the century (that is, Mod(NewYear, 100))

D = which century (that is, NewYear / 100)

W = (13 * A – 1) / 5

X = C / 4

Y = D / 4

Z = W + X + Y + B + C – 2 * D

R = Mod(Z, 7)
At this point, R is an Integer value between 0 and 6, inclusive:

R = 0 Sunday
R = 1 Monday
R = 2 Tuesday
R = 3 Wednesday
R = 4 Thursday
R = 5 Friday
R = 6 Saturday
Examples

Suppose the date is December 2, 2009. Then:

Month = 12

Day = 2

Year = 2009
so:

A = 10

B = 2

C = 9

D = 20

W = (13 * 10 – 1) / 5 = 129 / 5 = 25

X = 9 / 4 = 2

Y = 20 / 4 = 5

Z = 25 + 2 + 5 + 2 + 9 – 2 * 20 = 3

R = Mod((1, 0) = 3
and R = 3 gives us Wednesday.

Suppose instead the date is January 18, 2010. Then:

Month = 1

Day = 18

Year = 2010
so:

A = 11

B = 18

C = 9

D = 20

W = (13 * 11 – 1) / 5 = 143 / 5 = 28

X = 9 / 4 = 2

Y = 20 / 4 = 5

Z = 28 + 2 + 5 + 18 + 9 – 2 * 20 = 22

R = Mod(22, 7) = 1
and R = 1 gives us Monday.

Notes

There is a Wikipedia article on this subject which presents a similar (though not identical) version of the algorithm.

Other people have invented their own algorithms to do the same thing. (Some such algorithms are shorter. They are not necessarily easier to understand).

This uses the Gregorian calendar, which is our current standard. There are other calendars in use in the world. As the Gregorian calendar was devised in 1582, fixing the cumulative errors of the preceding Julian calendar, it is not clear that Zeller’s algorithm will work properly for dates before 1582.

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Entry filed under: .Friday, .Monday, .Mother_Goose, .Saturday, .Sunday, .Thursday, .Tuesday, .Wednesday, .week, Monday's Child. Tags: .

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