Doomsday rule

The Doomsdaymethode is a simple procedure to determine the weekday of a given date, which can be performed with mental arithmetic operations. It was developed around 1970 by the British mathematician John Horton Conway.

Is determined the day of the week on which the date falls after the Gregorian calendar. Thus, this method is initially only for the calculation of data from 15 October 1582., The calculation will be modified accordingly to the rest of the data according to the Julian calendar (see application in the Julian calendar ).

• 2.1 Calculation of the century doomsday
• 2.2 Calculation of the doomsday of one year

• 3.1 the week of 26 October 2005
• 3.2 the week of 26 February 1960

Calculation day of the week

The algorithm is based on the so-called Doomsday ( actual meaning of the word: " Day of Judgment " ), which, in this context, the last week of February the day ( ie the 28th or in a leap year 29 February ) is one year.

If you know the Doomsday, you can from the last day of February to count back as a fixed point of the week days for all other data for the year before and.

In practice, calculations come from week days in the current year or in the near past or the future is most commonly found. These calculations are quite easy to carry out in your head and are therefore presented here first.

For these calculations, the Doomsday should be learned by heart just for the current year. The Doomsday migrates every year on a weekday, in leap years two weeks days. Thus, the Doomsday for years in the recent past or future rather easily determined by forward and backward computation.

* Leap Year

Watch Rules for Doomsday

In addition, there are a number of mnemonic devices to facilitate the calculation:

• As of April falls in straight months, the day number of the month on the Doomsday ( 4 4th, 6th, 6th, 8th 8th, 10th 10th and 12th of 12 )
• The 9th of 5, 5 9, 11, 7 and 7 11 is a Doomsday. There is also an English mnemonic: " I work from 9 to 5 at the 7-11. " (7 -Eleven is an international retail chain. )

• 9 5
• 6 6
• 11 7
• 8 8
• 5 9
• 10 10
• 7 11
• 12 12

• In January in leap years January 4 a Doomsday, in other years it is the 3rd of January. ( Mnemonic: Holy 3 Kings; better: " It is three years, the 3, and leap years are divisible by 4. " )
• In February, it is the last day, ie the 28th or the 29th in a leap year.
• In March there are all divisible by 7 days, so the 7th, 14th, 21st and 28th

• The following months have the same sequence of days of the week: January (only in leap years ), April and July
• January and October (except in leap years)
• February (except in leap years), March and November
• February and August (only in leap years)
• September and December

In addition, one can notice more fixed data, such as December 24th always falls on the day which is two days before the Doomsday. Similarly, the custom birthday, name day, anniversary, etc., can be called as fixed data.

Memo list

The following memo list to memorize, and you can apply the Doomsday method.

Calculation of the doomsday

For years that are further in the past or future, the Doomsday can be determined by calculation, including also sufficient mental arithmetic.

The weekdays are interpreted as numbers as follows:

Calculation of the century doomsday

The starting point is the Doomsday of the first year in a century. Should be learned the Doomsday for the full centuries from 1800 to 2100 ( see table). Because there are days of the week every 400 years, can according to the previous or next expected to be for other centuries. One can also simply based on the Doomsday of the century, in which one is born (mostly so wednesday).

Based on the 400 -year cycle described above can alternatively make a calculation for the " Century Doomsday ": If we add the method described above, the Doomsday back to a fictional year 0, you get this as a result of the Tuesday, which thus box, is the "original Doomsday " for further calculation is based.

One must still calculate now

The result is multiplied by 2 then the number of days that you must now count back from Tuesday to get the Doomsday of the corresponding century.

Shown as formula arises from this:

,

Where stands for the year for which you want to calculate the century - Doomsday.

Calculation of the doomsday of one year

The calculation of the doomsday in a given year consists of four steps:

The results of the four steps will be added, wherein a multiple of 7 is peeled, so that a number from 0 to 6 results. This is the desired Doomsday of the year.

As a formula, the process can be represented as, where represents the last two digits of the year for which the Doomsday should be identified and called the " century - Doomsday " according to the above table or calculation follows:

Is the Doomsday determined as described above may be forwarded or on any date of the year back-calculated.

Alternatively, can be added to the integer result of the division by 4 of the same two -digit number plus the Jahrhundertdoomsday for the calculation of the doomsday in a given year, the last two digits. This sum is then divided modulo 7

However, the detour via the dozens is easier for quick mental calculation, because for the calculation of smaller numbers should be divided by 7.

Examples

The week of the 26th October 2005

The Doomsday in 2005 is calculated as follows:

The sum of the results of the four steps yields 0 5 1 2 = 8 Of these, 7 is subtracted, which results then 1, ie Monday.

The 10th of October, so a Monday (see rule of thumb ). Then the 24th is a Monday and the sought October 26, 2005 is a Wednesday.

The week of 26 February 1960

Total = 8 Of 7 deducted, the results then 1, ie Monday. Since 1960 was a leap year, February 29th is a Monday and therefore Submitted February 26, a Friday.

Application in the Julian calendar

In principle, this method can be applied analogously also for data according to the Julian calendar, as this from Gregorian leap years only by the regulation to "smooth" centuries (1800, 1900, etc.) is different.

For this purpose, however, must calculate the " century - doomsday " (see above) are adjusted as follows:

• The "original Doomsday " is Sunday.
• Is to calculate how often the year can be divided by 100 and
• This residue is divisible by 7.

The result is then calculated back from Sunday from:

Can then be further proceed as described above.

Monitoring of results

A simple and safe method of checking the results shown represent perpetual calendar

Others

Towards the end of the 19th century, many methods have been published for weekday calculation. The first release is probably the Lewis Carroll in the journal Nature (Vol. 35, March 31, 1887, p 517). It is basically very similar to the Doomsday method. It writes Carroll, "I myself am not a calculator and on average I need about 20 seconds to answer a question; but I have no doubt that a real calculator to answer would not even need 15 seconds. "