Vorlage:Ostern/Calc
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Diese Seite ist eine Untervorlage von Vorlage:Ostern. |
Herleitung
Gregorianischer Kalender
1. die Säkularzahl: K(X) = X div 100
2. die säkulare Mondschaltung: M(K) = 15 + (3K + 3) div 4 - (8K + 13) div 25
3. die säkulare Sonnenschaltung: S(K) = 2 - (3K + 3) div 4
4. den Mondparameter: A(X) = X mod 19
5. den Keim für den ersten Vollmond im Frühling: D(A,M) = (19A + M) mod 30
6. die kalendarische Korrekturgröße: R(D,A) = (D + A div 11) div 29
7. die Ostergrenze: OG(D,R) = 21 + D - R
8. den ersten Sonntag im März: SZ(X,S) = 7 - (X + X div 4 + S) mod 7
9. die Entfernung des OS von der Ostergrenze
(Osterentfernung in Tagen): OE(OG,SZ) = 7 - (OG - SZ) mod 7
10. das Datum des Ostersonntags als Märzdatum
(32. März = 1. April usw.): OS = OG + OE
Kompakt:
(SET 1)
1. K(X) = X div 100
2. M(K) = 15 + (3K + 3) div 4 - (8K + 13) div 25
3. S(K) = 2 - (3K + 3) div 4
4. A(X) = X mod 19
5. D(A,M) = (19A + M) mod 30
6. R(D,A) = (D + A div 11) div 29
7. OG(D,R) = 21 + D - R
8. SZ(X,S) = 7 - (X + X div 4 + S) mod 7
9. OE(OG,SZ) = 7 - (OG - SZ) mod 7
10. OS = OG + OE
"A div B" durch (floor(A/B)) ersetzen:
(SET 2)
1. K(X) = floor(X/100)
2. M(K) = 15 + (floor((3*K+3)/4)) - (floor((8*K + 13)/25))
3. S(K) = 2 - (floor((3*K+3)/4))
4. A(X) = X mod 19
5. D(A,M) = (19*A + M) mod 30
6. R(D,A) = (floor((D + (floor(A/11)))/29))
7. OG(D,R) = 21 + D - R
8. SZ(X,S) = 7 - ((X + (floor(X/4)) + S) mod 7)
9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)
10. OS = OG + OE
1 in 2 und 3 sowie 4 in 5 und 6:
(SET 3)
2. M(X) = 15 + (floor((3*(floor(X/100))+3)/4)) - (floor((8*(floor(X/100)) + 13)/25))
3. S(X) = 2 - (floor((3*(floor(X/100))+3)/4))
5. D(X,M) = (19*(X mod 19) + M) mod 30
6. R(D,X) = (floor((D + (floor((X mod 19)/11)))/29))
7. OG(D,R) = 21 + D - R
8. SZ(X,S) = 7 - ((X + (floor(X/4)) + S) mod 7)
9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)
10. OS = OG + OE
2 in 5 sowie 3 in 8:
(SET 4)
5. D(X) = (19*(X mod 19) + (15 + (floor((3*(floor(X/100))+3)/4)) - (floor((8*(floor(X/100)) + 13)/25)))) mod 30
6. R(D,X) = (floor((D + (floor((X mod 19)/11)))/29))
7. OG(D,R) = 21 + D - R
8. SZ(X) = 7 - ((X + (floor(X/4)) + (2 - (floor((3*(floor(X/100))+3)/4)))) mod 7)
9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)
10. OS = OG + OE
5 in 6 und 7:
(SET 5)
6. R(X) = (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))
7. OG(X,R) = 21 + ((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - R
8. SZ(X) = 7 - ((X + (floor(X/4)) + (2 - (floor((3*(floor(X/100))+3)/4)))) mod 7)
9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)
10. OS = OG + OE
6 in 7:
(SET 6)
7. OG(X) = 21 + ((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))
8. SZ(X) = 7 - ((X + (floor(X/4)) + (2 - (floor((3*(floor(X/100))+3)/4)))) mod 7)
9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)
10. OS = OG + OE
8 in 9:
(SET 7)
7. OG(X) = 21 + ((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))
9. OE(OG,X) = 7 - ((OG - (7-((X+(floor(X/4))+(2-(floor((3*(floor(X/100))+3)/4)))) mod 7))) mod 7)
10. OS = OG + OE
7 in 9 und 10:
(SET 8)
9. OE(X) = 7-(((21+((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))) - (7-((X+(floor(X/4))+(2-(floor((3*(floor(X/100))+3)/4)))) mod 7))) mod 7)
10. OS(X,OE) = (21+((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))) + OE
9 in 10:
(SET 9)
10. OS(X) = (21+((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))) + (7-(((21+((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30) - (floor((((19*(X mod 19)+(15+(floor((3*(floor(X/100))+3)/4))-(floor((8*(floor(X/100))+13)/25)))) mod 30)+(floor((X mod 19)/11)))/29))) - (7-((X+(floor(X/4))+(2-(floor((3*(floor(X/100))+3)/4)))) mod 7))) mod 7))
Julianischer Kalender
Für den Julianischen Kalender gelten die Konstanten M = 15 und S = 0. Diese in SET 2 eingesetzt ergibt für SET 5:
(SET 5a) 5. D(X) = (19*(X mod 19) + 15) mod 30 6. R(D,X) = (floor((D + (floor((X mod 19)/11)))/29)) 7. OG(D,R) = 21 + D - R 8. SZ(X) = 7 - ((X + (floor(X/4))) mod 7) 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7) 10. OS = OG + OE 5 in 6 und 7: (SET 6a) 6. R(X) = (floor((((19*(X mod 19) + 15) mod 30) + (floor((X mod 19)/11)))/29)) 7. OG(X,R) = 21 + ((19*(X mod 19) + 15) mod 30) - R 8. SZ(X) = 7 - ((X + (floor(X/4))) mod 7) 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7) 10. OS(OG,OE) = OG + OE 6 in 7: (SET 7a) 7. OG(X) = 21 + ((19*(X mod 19) + 15) mod 30) - (floor((((19*(X mod 19) + 15) mod 30) + (floor((X mod 19)/11)))/29)) 8. SZ(X) = 7 - ((X + (floor(X/4))) mod 7) 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7) 10. OS(OG,OE) = OG + OE 8 in 9: (SET 8a) 7. OG(X) = 21 + ((19*(X mod 19) + 15) mod 30) - (floor((((19*(X mod 19) + 15) mod 30) + (floor((X mod 19)/11)))/29)) 9. OE(OG,X) = 7 - ((OG - (7 - ((X + (floor(X/4))) mod 7))) mod 7) 10. OS(OG,OE) = OG + OE 7 in 9 und 10: (SET 9a) 9. OE(X) = 7 - (((21+((19*(X mod 19)+15) mod 30) - (floor((((19*(X mod 19)+15) mod 30) + (floor((X mod 19)/11)))/29))) - (7 - ((X + (floor(X/4))) mod 7))) mod 7) 10. OS(OE,X) = (21+((19*(X mod 19)+15) mod 30) - (floor((((19*(X mod 19)+15) mod 30) + (floor((X mod 19)/11)))/29))) + OE 9 in 10: (SET 10) 10. OS(X) = (21+((19*(X mod 19)+15) mod 30)-(floor((((19*(X mod 19)+15) mod 30)+(floor((X mod 19)/11)))/29)))+(7-(((21+((19*(X mod 19)+15) mod 30)-(floor((((19*(X mod 19)+15) mod 30)+(floor((X mod 19)/11)))/29)))-(7-((X +(floor(X/4))) mod 7))) mod 7))