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From: Stephen Hayes
To: All
Date: 2004-03-27 02:45:12
Subject: Calendar

[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]
 

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