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	{{Template:TI-BASIC:Routine		{{Template:TI-BASIC:Routine
	\|picture=@@		\|picture=
	\|summary=Calculates the day that Easter Sunday falls on any given year.		\|summary=Calculates the day that Easter Sunday falls on any given year.
	\|input=''Y'' - The year (any year at all)		\|input=''Y'' - The year (any year at all)
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	\|compatibility=TI-83/84/+/SE		\|compatibility=TI-83/84/+/SE
	\|author=John Horton Conway		\|author=John Horton Conway
	\|authors=@@		\|authors=
	\|url=http://web.math.princeton.edu/facultypapers/Conway/		\|url=http://web.math.princeton.edu/facultypapers/Conway/
	\|download=[file eastercalculation.zip]		\|download=[file eastercalculation.zip]

Maintenance script: Initial automated import

2016-02-24T18:06:08Z

Initial automated import

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{{Template:TI-BASIC:Routine
|picture=@@
|summary=Calculates the day that Easter Sunday falls on any given year.
|input=''Y'' - The year (any year at all)
|output=''Ans'' - The day in March of Easter Sunday (plus 31 if the month is April)
|variable=Y, Ans
|compatibility=TI-83/84/+/SE
|author=John Horton Conway
|authors=@@
|url=http://web.math.princeton.edu/facultypapers/Conway/
|download=[file 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

[http://latex.codecogs.com/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''':

[http://latex.codecogs.com/gif.latex?G%3D%28Y%5Cmod19%29+1]

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

[http://latex.codecogs.com/gif.latex?C%3D-H+%5BH/4%5D+%5B8%28H+11%29/25%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 [[TI-BASIC:Day_Of_Week_Alternative|Day of Week routine.]][[TI-BASIC:Footnote|Footnote]] If you have an 84+ or 84+SE, this may as well be {{Ans+7-dayOfWk(Y,3+(Ans>31),Ans31(Ans>31))}}. [[TI-BASIC:/footnote|/footnote]]

= Error Conditions =

* None known.

= Related Routines =

* [[TI-BASIC:Day_Of_Week_Alternative|Day of Week (Alternative)]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Easter Calculation - Revision history

Maintenance script: Automated @@ correction

Maintenance script: Initial automated import