Easter Calculation

Routine Summary

Calculates the day that Easter Sunday falls on any given year.

Inputs

Y - The year (any year at all)

Outputs

Ans - The day in March of Easter Sunday (plus 31 if the month is April)

Variables Used

Y, Ans

Calculator Compatibility

TI-83/84/+/SE

Author

John Horton Conway

URL: [http://web.math.princeton.edu/facultypapers/Conway/]

Download

eastercalculation.zip

:int(Y/ᴇ2
:50-30fPart((11(1+19fPart(Y/19))-Ans+int(Ans/4)+int(8(Ans+11)/25))/30
:If Ans=50 or Ans=49 and 11≤19fPart(Y/19
:Ans-1
:round(Ans+7-7fPart((int(23(3+(Ans>31))/9)+Ans-31(Ans>31)+2+Y+int(Y/4)-int(Y/ᴇ2)+int(Y/400))/7),0

This is the TI-BASIC version of an Easter Calculation algorithm by John Horton Conway (famous for creating the cellular automata "The Game of Life"). After implementation of this program, 3+(Ans>31) is the month it occurs in, and Ans-31(Ans>31) is the day.

Date Identification

This code, as it stands right now, displays the day of March it falls on (if it's over 31, then the day in April+31).

Append the following code to display the actual day:

:ClrHome
:Disp sub("MARCHAPRIL",1+5(Ans>31),5
:Output(1,7,Ans-31(Ans>31

Why it Works

Easter is the first Sunday strictly after the Paschal Full Moon, which is an approximation of the real full moon (the 14th day of a lunar month, specifically), although it may be off by as much as two days.

The formula is

gif.latex?%28April%5C%3B19%3DMarch%5C%3B50%29-%28%2811G+C%29%5Cmod30%29

except if the formula gives April 19, take April 18, and if the formula gives you April 18 and G≥12, take April 17.

Here is the value of G:

gif.latex?G%3D%28Y%5Cmod19%29+1

Here is the value of C (with H=int(Y/100), and [H]=int(H)):

25%5D

The first four lines of code implement this algorithm.

Lastly, the last line of code adjusts the date to the next Sunday using a modified version of the Day of Week routine.1

Error Conditions

  • None known.

Related Routines

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