Dominical Letter - Use For Mental Calculation

Use For Mental Calculation

There exist patterns in the dominical letters, which are very useful for mental calculation.

Patterns for years:

To use these patterns, choose and remember a year to use as a starting point, such as 2000=BA.

Note that because of the complicated Gregorian leap-year rules, these patterns break near some century changes. Note the reverse alphabetical order.

1992 3 4 5 96 7 8 9 2000 1 2 3 04 5 6 7 08 9 0 1 2012 3 ED C B A GF E D C BA G F E DC B A G FE D C B AG F

and

(note the reversed order of the years as well as of the letters) 2040 2030 2020 2010 2000 1990 1980 1970 1960 1950 AG F ED C BA G FE D CB A | | | | | | | | | | G FE D CB A GF E DC B AG 2046 2036 2026 2016 2006 1996 1986 1976 1966 1956

Patterns for days of the month:

The dominical letters for the first day of each month form the nonsense mnemonic phrase "Add G, beg C, fad F".

The following dates, given in day/month form, all have dominical letter C: 4/4, 6/6, 8/8, 10/10, 12/12, 9/5, 5/9, 11/7, 7/11 (see also the Doomsday rule).

We are able to calculate the Dominical letter in this way (function in C), where:

• m = month
• y = year
• s = "style"; 0 for Julian, otherwise Gregorian.

char dominical(int m,int y,int s){ int leap; int a,b; leap=(s==0&&y%4==0)||(s!=0&&(y%4==0&&y%100!=0||y%400==0)); a=(y%100)%28; b=(s==0)*(4+(y%700)/100+2*(a/4)+6*((!leap)*(1+(a%4))+(leap)*((9+m)/12)))%7+ (s!=0)*(2*(1+(y%400)/100+(a/4))+6*((!leap)*(1+(a%4))+(leap)*((9+m)/12)))%7; b=(b==0)*(b+7)+(b!=0)*b; return (char)(64+b); }