[Part 1 of 5] NOTES on the CALENDAR ~~~~~~~~~~~~~~~~~~~~~ The intention of this document is to provide information on the calendar for computer programmers or others who may need to do calculations involving calendar dates, or who may need to verify that a given date validly represents some actual historical day. 1. TERMINOLOGY USED The following terms, when used in this document, have the meanings given here. Some further expansion of these definitions may be found in later sections. The terms are presented in alphabetical order. AD - Anno Domini (in the year of the Lord), prefixed to the number designating a year in the christian era. AND - a mathematical symbol (from the programming language PASCAL) meaning that the conditions to the left and the right must both be true. AUC - Ab Urbe Condita (from the foundation of the city), suffixed to the number designating a year in the Roman (republican and imperial) civil calendar. BC - Before Christ, suffixed to the number designating a year in the pre-christian era. Calendar - a system for numbering and counting the cycles of days, months and years. DIV - a mathematical symbol (from the programming language PASCAL) meaning integer division of the term to the left of DIV by the term to the right of DIV, where integer division means division with any remainder (however large) ignored; for example "a DIV b" means the integer quotient of `a' divided by `b', the remainder being ignored, or 13 DIV 7 = 1. Gregorian - the calendar now in use throughout the world and also known as the New (or New-style) Calendar. Julian - the calendar in use throughout Christendom until AD 1582 and in England (and other places) until AD 1752 and also known as the Old (or Old-style) Calendar. Leap year - any year which is one day longer than the standard year of the calendar in use. MOD - a mathematical symbol (from the programming language PASCAL) meaning the remainder which results from the division of the term to the left of MOD by the term to the right of MOD; for example "a MOD b" means the remainder of `a' divided by `b', the quotient being ignored, or 13 MOD 7 = 6. Month - the major subdivision of a year; in all calendars considered here there are twelve months in every year with varying numbers of days in each month - this document uses the modern English names of the months (sometimes abbreviated to the first three letters of the name) or their modern numbers (January = 1, February = 2, etc) throughout. OR - a mathematical symbol (from the programming language PASCAL) meaning that the conditions to the left and the right may either or both be true. Week - the seven-day cycle of days starting on Sunday and ending on Saturday; this is independent of the cycles of months and years and has Jewish and other origins - this document uses the modern English names of the days of the week. <> - a mathematical symbol (from the programming language PASCAL) meaning "is not equal to". * - a mathematical symbol (from the programming language PASCAL) meaning "multiplied by". ( ) - parentheses and other mathematical symbols not explicitly defined here have their normal mathematical meanings and significances. 2. BASIC ASSUMPTIONS The following statements are assumed to be facts - the interested reader may verify them from various reference sources. For brevity the sources are mostly not quoted here. 2.1 THE WEEK The seven-day cycle is of very ancient origin (Jewish and other). a) The individual days are numbered and named as follows. 1 Sunday 2 Monday 3 Tuesday 4 Wednesday 5 Thursday 6 Friday 7 Saturday b) At different times and in different places the names of the days may vary. c) This cycle has not been broken or in any way disturbed within the period of any calendar discussed here. Consequently any system for calculating the day of the week from the date must result in Friday when applied to 3rd April AD 33 (the traditional date of the Crucifixion, Good Friday). [It is neither important for the purpose of this document to believe in the historical accuracy of any traditional dates, nor in the truth or otherwise of any events. It is necessary to know what the traditions are and at least their mathematical significances. Such dates are the basis of any calendar and are used here for the purpose of calculation.] 2.2 THE ROMAN CIVIL CALENDAR In 46 BC Julius Caesar regularized the civil calendar of the Roman republic to make it operate as follows. a) Every year was divided into twelve months which were numbered as follows and to which we assign the following modern names. 1 January 2 February 3 March 4 April 5 May 6 June 7 July 8 August 9 September 10 October 11 November 12 December b) The years were numbered AUC (from the date of the foundation of the city of Rome). c) Every fourth year was to have one extra day in February. However, the Roman civil authorities responsible for the calendar mismanaged it after Caesar's death, keeping a leap year every third year, so by 8 BC three days had been gained. [continued in part 2] --- WtrGate v0.93.p9 Unreg * Origin: Khanya BBS, Tshwane, South Africa [012] 333-0004 (5:7106/20) SEEN-BY: 633/267 270 @PATH: 7106/20 22 140/1 106/2000 633/267