Easter Holiday formulas -- How do they do it!? [low priority post]

macropod · #1 11-10-2022, 02:55 PM

In the western calendar, Easter dates follow the 19-year lunar cycle, hence the 19 in the formulae.

Do note that those formulae don't correctly calculate Easter dates for the orthodox churches. Orthodox churches celebrate Easter on the basis of the Julian calendar. Until the Gregorian calendar was introduced in 1582, Orthodox churches celebrated Easter Sunday on the same date as Western churches. Since then, the Orthodox churches have often celebrated Easter Sunday on different dates from Western churches. In some years the Orthodox Easter Sunday occurs on the same day as the Western Easter Sunday. In most years, however, Orthodox Easter follows Western Easter by at least one week.

In Word, you can do both sets of Easter calculations, with fields coded as:

Code:

{QUOTE
{ASK Year "For what Year do you want the date of Easter?" \d {DATE \@ YYYY}}
{SET yr{Year}}
{SET a{=MOD(yr,19)}}
{SET b{=INT(yr/100)}}
{SET c{=MOD(yr,100)}}
{SET d{=INT(b/4)}}
{SET e{=MOD(b,4)}}
{SET f{=(b+8)/25}}
{SET g{=INT((b-f+1)/3)}}
{SET h{=MOD((19*a+b-d-g+15),30)}}
{SET i{=INT(c/4)}}
{SET k{=MOD(c,4)}}
{SET l{=MOD((32+2*e+2*i-h-k),7)}}
{SET m{=INT((a+11*h+22*l)/451)}}
{SET Gm{=INT((h+l-7*m+114)/31)}}
{SET Gd{=MOD((h+l-7*m+114),31)+1}}
"In {yr}, the Western Easter Sunday {={QUOTE"{yr}{Gm \# 00}{Gd \# 00}" \@ YYYYMMdd }-{DATE \@ YYYYMMdd} \# falls;fell} on the (Gregorian) {Gd \* Ordinal} of {QUOTE "{Gm}/0" \@ MMMM}."}

and:

Code:

{QUOTE
{SET G{=MOD(yr,19)}}
{SET I{=MOD((19*G+15),30)}}
{SET J{=MOD((yr+INT(yr/4)+I),7)}}
{SET Om{=3+INT((I-J+40)/44)}}
{SET Od{=I-J+28-31*INT(Om/4)}}
{SET a{=INT((14-Om)/12)}}
{SET b{=yy+4800-a}}
{SET c{=Om+12*a-3}}
{SET jd{=Od+INT((153*c+2)/5)+365*b+INT(b/4)-32083}}
{SET e{=INT((4*(jd+32044)+3)/146097)}}
{SET f{=jd+32044-INT(146097*e/4)}}
{SET g{=INT((4*f+3)/1461)}}
{SET h{=f-INT(1461*g/4)}}
{SET i{=INT((5*h+2)/153)}}
{SET Gd1{=h-INT((153*i+2)/5)+1}}
{SET Gm1{=i+3-12*INT(i/10)}}
"In the same year, the Orthodox Easter Sunday {={QUOTE"{yr}{Gm1 \# 00}{Gd1 \# 00}" \@ YYYYMMdd }-{DATE \@ YYYYMMdd} \# falls;fell} on the (Julian) {Od \* Ordinal} of {QUOTE "{Om}/0" \@ MMMM}. This equates to the (Gregorian) {Gd1 \* Ordinal} of {QUOTE "{Gm1}/0" \@ MMMM}."}

For those who are interested about the Orthodox Easter date calculation, in the above field:
G is the so-called “Golden Number”-1
I is the number of days from 21 March to the Paschal full moon
J is the weekday of the Paschal full moon (0=Sunday, 1=Monday, etc.)

I-J is the number of days from 21 March to the Sunday on or before the Paschal full moon.

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