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Editing Ordinal date

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The table of month lengths can be replaced following the method of encoding the month-length variation in [[Zeller's congruence]]. As in Zeller, the {{mvar|m}} is changed to {{math|''m'' + 12}} if {{math| ''m'' &leq; 2}}. It can be shown (see below) that for a month-number {{mvar|m}}, the total days of the preceding months is equal to {{math|⌊(153 * (''m'' &minus; 3) + 2) / 5⌋}}. As a result, the March 1-based ordinal day number is {{math|1=''O''<sub>Mar</sub> = ⌊(153 × (''m'' &minus; 3) + 2) / 5⌋ + ''d''}}.
The table of month lengths can be replaced following the method of encoding the month-length variation in [[Zeller's congruence]]. As in Zeller, the {{mvar|m}} is changed to {{math|''m'' + 12}} if {{math| ''m'' &leq; 2}}. It can be shown (see below) that for a month-number {{mvar|m}}, the total days of the preceding months is equal to {{math|⌊(153 * (''m'' &minus; 3) + 2) / 5⌋}}. As a result, the March 1-based ordinal day number is {{math|1=''O''<sub>Mar</sub> = ⌊(153 × (''m'' &minus; 3) + 2) / 5⌋ + ''d''}}.


The formula reflects the fact that any five consecutive months in the range March–January have a total length of 153&nbsp;days, due to a fixed pattern 31–30–31–30–31 repeating itself twice. This is similar to encoding of the month offset (which would be the same sequence modulo&nbsp;7) in Zeller's congruence. As {{sfrac|153|5}} is 30.6, the sequence oscillates in the desired pattern with the desired period&nbsp;5.
The formula reflects the fact that any five consecutive months in the range March–January have a total length of 153&nbsp;days, due to a fixed pattern 31–30–31–30–31 repeating itself twice. This is similar to encoding of the month offset (which would be the same sequence modulo&nbsp;7) in [[Zeller's congruence]]. As {{sfrac|153|5}} is 30.6, the sequence oscillates in the desired pattern with the desired period&nbsp;5.


To go from the March 1 based ordinal day to a January 1 based ordinal day:
To go from the March 1 based ordinal day to a January 1 based ordinal day:
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Latin: A a Á á À à  â Ä ä Ǎ ǎ Ă ă Ā ā à ã Å å Ą ą Æ æ Ǣ ǣ   B b   C c Ć ć Ċ ċ Ĉ ĉ Č č Ç ç   D d Ď ď Đ đ Ḍ ḍ Ð ð   E e É é È è Ė ė Ê ê Ë ë Ě ě Ĕ ĕ Ē ē Ẽ ẽ Ę ę Ẹ ẹ Ɛ ɛ Ǝ ǝ Ə ə   F f   G g Ġ ġ Ĝ ĝ Ğ ğ Ģ ģ   H h Ĥ ĥ Ħ ħ Ḥ ḥ   I i İ ı Í í Ì ì Î î Ï ï Ǐ ǐ Ĭ ĭ Ī ī Ĩ ĩ Į į Ị ị   J j Ĵ ĵ   K k Ķ ķ   L l Ĺ ĺ Ŀ ŀ Ľ ľ Ļ ļ Ł ł Ḷ ḷ Ḹ ḹ   M m Ṃ ṃ   N n Ń ń Ň ň Ñ ñ Ņ ņ Ṇ ṇ Ŋ ŋ   O o Ó ó Ò ò Ô ô Ö ö Ǒ ǒ Ŏ ŏ Ō ō Õ õ Ǫ ǫ Ọ ọ Ő ő Ø ø Œ œ   Ɔ ɔ   P p   Q q   R r Ŕ ŕ Ř ř Ŗ ŗ Ṛ ṛ Ṝ ṝ   S s Ś ś Ŝ ŝ Š š Ş ş Ș ș Ṣ ṣ ß   T t Ť ť Ţ ţ Ț ț Ṭ ṭ Þ þ   U u Ú ú Ù ù Û û Ü ü Ǔ ǔ Ŭ ŭ Ū ū Ũ ũ Ů ů Ų ų Ụ ụ Ű ű Ǘ ǘ Ǜ ǜ Ǚ ǚ Ǖ ǖ   V v   W w Ŵ ŵ   X x   Y y Ý ý Ŷ ŷ Ÿ ÿ Ỹ ỹ Ȳ ȳ   Z z Ź ź Ż ż Ž ž   ß Ð ð Þ þ Ŋ ŋ Ə ə
Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ   Α α Β β Γ γ Δ δ   Ε ε Ζ ζ Η η Θ θ   Ι ι Κ κ Λ λ Μ μ   Ν ν Ξ ξ Ο ο Π π   Ρ ρ Σ σ ς Τ τ Υ υ   Φ φ Χ χ Ψ ψ Ω ω   {{Polytonic|}}
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