https://wiki.schmino.de/index.php?action=history&feed=atom&title=Vorlage%3AOstern%2FCalc 2026-04-27T11:40:31Z Versionsgeschichte dieser Seite in KyllburgWiki MediaWiki 1.45.1 https://wiki.schmino.de/index.php?title=Vorlage:Ostern/Calc&diff=2493&oldid=prev 2016-01-06T19:59:21Z

<p>Die Seite wurde neu angelegt: „{{Dokumentation/Unterseite}} &lt;onlyinclude&gt;&lt;includeonly&gt;{{#ifexpr:{{{1}}} &gt; 1582|{{#expr:((21+((19*({{{1}}} mod 19)+(15+(floor((3*(floor({{{1}}}/100))+3)/4))-(…“</p> <p><b>Neue Seite</b></p><div>{{Dokumentation/Unterseite}}<br /> <br /> &lt;onlyinclude&gt;&lt;includeonly&gt;{{#ifexpr:{{{1}}} &gt; 1582|{{#expr:((21+((19*({{{1}}} mod 19)+(15+(floor((3*(floor({{{1}}}/100))+3)/4))-(floor((8*(floor({{{1}}}/100))+13)/25)))) mod 30) - (floor((((19*({{{1}}} mod 19)+(15+(floor((3*(floor({{{1}}}/100))+3)/4))-(floor((8*(floor({{{1}}}/100))+13)/25)))) mod 30)+(floor(({{{1}}} mod 19)/11)))/29))) + (7-(((21+((19*({{{1}}} mod 19)+(15+(floor((3*(floor({{{1}}}/100))+3)/4))-(floor((8*(floor({{{1}}}/100))+13)/25)))) mod 30) - (floor((((19*({{{1}}} mod 19)+(15+(floor((3*(floor({{{1}}}/100))+3)/4))-(floor((8*(floor({{{1}}}/100))+13)/25)))) mod 30)+(floor(({{{1}}} mod 19)/11)))/29))) - (7-(({{{1}}}+(floor({{{1}}}/4))+(2-(floor((3*(floor({{{1}}}/100))+3)/4)))) mod 7))) mod 7)))}}|{{#expr:(21+((19*({{{1}}} mod 19)+15) mod 30)-(floor((((19*({{{1}}} mod 19)+15) mod 30)+(floor(({{{1}}} mod 19)/11)))/29)))+(7-(((21+((19*({{{1}}} mod 19)+15) mod 30)-(floor((((19*({{{1}}} mod 19)+15) mod 30)+(floor(({{{1}}} mod 19)/11)))/29)))-(7-(({{{1}}} +(floor({{{1}}}/4))) mod 7))) mod 7))}}}}&lt;/includeonly&gt;&lt;/onlyinclude&gt;<br /> <br /> == Herleitung ==<br /> === Gregorianischer Kalender ===<br /> &lt;pre style=&quot;white-space:pre-wrap;&quot;&gt; <br /> 1. die Säkularzahl: K(X) = X div 100<br /> 2. die säkulare Mondschaltung: M(K) = 15 + (3K + 3) div 4 - (8K + 13) div 25<br /> 3. die säkulare Sonnenschaltung: S(K) = 2 - (3K + 3) div 4<br /> 4. den Mondparameter: A(X) = X mod 19<br /> 5. den Keim für den ersten Vollmond im Frühling: D(A,M) = (19A + M) mod 30<br /> 6. die kalendarische Korrekturgröße: R(D,A) = (D + A div 11) div 29<br /> 7. die Ostergrenze: OG(D,R) = 21 + D - R<br /> 8. den ersten Sonntag im März: SZ(X,S) = 7 - (X + X div 4 + S) mod 7<br /> 9. die Entfernung des OS von der Ostergrenze<br /> (Osterentfernung in Tagen): OE(OG,SZ) = 7 - (OG - SZ) mod 7<br /> 10. das Datum des Ostersonntags als Märzdatum<br /> (32. März = 1. April usw.): OS = OG + OE<br /> <br /> Kompakt:<br /> <br /> (SET 1)<br /> 1. K(X) = X div 100<br /> 2. M(K) = 15 + (3K + 3) div 4 - (8K + 13) div 25<br /> 3. S(K) = 2 - (3K + 3) div 4<br /> 4. A(X) = X mod 19<br /> 5. D(A,M) = (19A + M) mod 30<br /> 6. R(D,A) = (D + A div 11) div 29<br /> 7. OG(D,R) = 21 + D - R<br /> 8. SZ(X,S) = 7 - (X + X div 4 + S) mod 7<br /> 9. OE(OG,SZ) = 7 - (OG - SZ) mod 7<br /> 10. OS = OG + OE<br /> <br /> &quot;A div B&quot; durch (floor(A/B)) ersetzen:<br /> <br /> (SET 2)<br /> 1. K(X) = floor(X/100)<br /> 2. M(K) = 15 + (floor((3*K+3)/4)) - (floor((8*K + 13)/25))<br /> 3. S(K) = 2 - (floor((3*K+3)/4))<br /> 4. A(X) = X mod 19<br /> 5. D(A,M) = (19*A + M) mod 30<br /> 6. R(D,A) = (floor((D + (floor(A/11)))/29))<br /> 7. OG(D,R) = 21 + D - R<br /> 8. SZ(X,S) = 7 - ((X + (floor(X/4)) + S) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 1 in 2 und 3 sowie 4 in 5 und 6:<br /> <br /> (SET 3)<br /> 2. M(X) = 15 + (floor((3*(floor(X/100))+3)/4)) - (floor((8*(floor(X/100)) + 13)/25))<br /> 3. S(X) = 2 - (floor((3*(floor(X/100))+3)/4))<br /> 5. D(X,M) = (19*(X mod 19) + M) mod 30<br /> 6. R(D,X) = (floor((D + (floor((X mod 19)/11)))/29))<br /> 7. OG(D,R) = 21 + D - R<br /> 8. SZ(X,S) = 7 - ((X + (floor(X/4)) + S) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 2 in 5 sowie 3 in 8:<br /> <br /> (SET 4)<br /> 5. D(X) = (19*(X mod 19) + (15 + (floor((3*(floor(X/100))+3)/4)) - (floor((8*(floor(X/100)) + 13)/25)))) mod 30<br /> 6. R(D,X) = (floor((D + (floor((X mod 19)/11)))/29))<br /> 7. OG(D,R) = 21 + D - R<br /> 8. SZ(X) = 7 - ((X + (floor(X/4)) + (2 - (floor((3*(floor(X/100))+3)/4)))) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 5 in 6 und 7:<br /> <br /> (SET 5)<br /> 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))<br /> 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<br /> 8. SZ(X) = 7 - ((X + (floor(X/4)) + (2 - (floor((3*(floor(X/100))+3)/4)))) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 6 in 7:<br /> <br /> (SET 6)<br /> 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))<br /> 8. SZ(X) = 7 - ((X + (floor(X/4)) + (2 - (floor((3*(floor(X/100))+3)/4)))) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 8 in 9:<br /> <br /> (SET 7)<br /> 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))<br /> 9. OE(OG,X) = 7 - ((OG - (7-((X+(floor(X/4))+(2-(floor((3*(floor(X/100))+3)/4)))) mod 7))) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 7 in 9 und 10:<br /> <br /> (SET 8)<br /> 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)<br /> 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<br /> <br /> 9 in 10:<br /> <br /> (SET 9)<br /> 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))<br /> &lt;/pre&gt;<br /> === Julianischer Kalender ===<br /> Für den Julianischen Kalender gelten die Konstanten M = 15 und S = 0. Diese in SET 2 eingesetzt ergibt für SET 5:<br /> <br /> &lt;pre style=&quot;white-space:pre-wrap;&quot;&gt; <br /> <br /> (SET 5a)<br /> 5. D(X) = (19*(X mod 19) + 15) mod 30<br /> 6. R(D,X) = (floor((D + (floor((X mod 19)/11)))/29))<br /> 7. OG(D,R) = 21 + D - R<br /> 8. SZ(X) = 7 - ((X + (floor(X/4))) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS = OG + OE<br /> <br /> 5 in 6 und 7:<br /> <br /> (SET 6a)<br /> 6. R(X) = (floor((((19*(X mod 19) + 15) mod 30) + (floor((X mod 19)/11)))/29))<br /> 7. OG(X,R) = 21 + ((19*(X mod 19) + 15) mod 30) - R<br /> 8. SZ(X) = 7 - ((X + (floor(X/4))) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS(OG,OE) = OG + OE<br /> <br /> 6 in 7: <br /> <br /> (SET 7a)<br /> 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))<br /> 8. SZ(X) = 7 - ((X + (floor(X/4))) mod 7)<br /> 9. OE(OG,SZ) = 7 - ((OG - SZ) mod 7)<br /> 10. OS(OG,OE) = OG + OE<br /> <br /> 8 in 9:<br /> <br /> (SET 8a)<br /> 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))<br /> 9. OE(OG,X) = 7 - ((OG - (7 - ((X + (floor(X/4))) mod 7))) mod 7)<br /> 10. OS(OG,OE) = OG + OE<br /> <br /> 7 in 9 und 10:<br /> <br /> (SET 9a)<br /> 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)<br /> 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<br /> <br /> 9 in 10:<br /> <br /> (SET 10)<br /> 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))<br /> &lt;/pre&gt;</div>

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