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-\documentclass{article}
-\nofiles
-
-\renewcommand{\div}{\rm\,div\,}\newcommand{\mod}{\rm\,mod\,}
-\newcommand{\dfrac}{\displaystyle\frac}
-
-\begin{document}
-
-\section*{\texttt{ReadMe} file --- Instructions}
-
-This file explains the use of \verb|CalXXXX.tex| and \verb|Cal2000.tex| files, possible
-modifications and gives the mathematical background for the calculation of the calendar. Both files
-are for \LaTeXe, and use the \verb|array.sty| package. At the end, there are some interesting
-numerical values and historical facts.
-
-\subsection*{The use}
-
-To print a calendar for a given year, use \verb|CalXXXX.tex| file. \LaTeXe it, type in the year
-(for example 2002), and the calendar for that year is produced. For the year B. C., enter the
-negative number (for example $-6$), and for the current year, \number\year th, you can press the
-ENTER key only.
-
-To print calendar for the years 1990--2020, use \verb|Cal2000.tex| file. \LaTeXe it and you will
-have the calendar for all that years.
-
-\subsection*{Possible modifications}
-
-In both files there is a peace of code clearly denoted for safe modifications.
-
-In \verb|CalXXXX.tex|, the most important changes are for a language: \verb|\Jan|, \dots
-\verb|\Dec| define names of the months. You can also set type of the calendar: Gregorian
-(\verb|\Julianfalse|) or Julian (\verb|\Juliantrue|). For details, see explanations later. Some
-misunderstanding could be for 0th year; normally it doesn't exist (before 1st is a $-1$st year),
-but if, for some reason, you need a 0th year, set \verb|\ZeroExisttrue| and the 0th year will exist
-(before 1st is 0th, and before it $-1$st). \verb|\BC| and \verb|\AD| are text after the year (in
-English, $-6$th year is 6~BC and 6th year is 6~AD).
-
-In the \verb|Cal2000.tex|, the most important changes are also for a language. Change definition
-for \verb|\YearMonths| and \verb|\Day| according to your language.
-
-Both files have a command \verb|\CmRulefalse|. If you change it to a \verb|\CmRuletrue|, you will
-see a centimeter scale at the right edge.
-
-Beside of these, other modifications are possible, but not recommended.
-
-\subsection*{Mathematical background}
-
-In both files, the day $x$ (0 for Sunday, 1 for Monday, etc.) for a date $d.m.y$ is calculated as
-\[ x=\left\{\begin{array}{ll}
-         x_0 \mod 7 & \mbox{if $m<3$} \\ (x_0-(4m+23) \div 10) \mod 7 & \mbox{if $m\ge3$}
-     \end{array}\right. \]
-where
-\[x_0=365y+31m+d+3+k \div 4-(k \div 100+1)\cdot3 \div 4\]
-and
-\[ k=\left\{\begin{array}{ll} y-1 & \mbox{if $m<3$}\\ y & \mbox{if $m\ge3$} \end{array}\right.\]
-
-This formulae are used in both files. In \verb|CalXXXX.tex|, you can see how \TeX calculates. In
-\verb|Cal2000.tex|, since the years 1990--2020 are fixed, there is no need to calculate anything,
-but the first day for all months for the years 1990--2020, are produced with the following Pascal
-code:
-
-\begin{verbatim}
-program cal(output);
-var x,y,m,k: longint;
-begin writeln('Year   J F M A M J J A S O N D');
-  for y:=1990 to 2020 do
-  begin write(y,'  ');
-    for m:=1 to 12 do
-    begin x:=365*y+31*m+4; { 4=d+3 }
-      if m<3 then k:=y-1 else k:=y;
-      x:=x+k div 4-(k div 100+1)*3 div 4;
-      if m>=3 then x:=x-(4*m+23) div 10;
-      x:=x mod 7;
-      write(' ',x)
-    end; writeln;
-  end;
-end.
-\end{verbatim}
-
-\subsection*{Numerical values}
-
-The lengths of solar (tropical) year and lunar month in days are
-\[ Y=365.24219872,\quad M=29.530588. \]
-(These are values for a period December 31st, 1900, at 12h --- since it slowly decreases.) The
-solar calendar should have about 365.24 days in a year (on average), while the lunar calendar
-should have months of 29.5 days (usually, 30 and 29 alternately). The lunisolar calendar should
-have both, but the ratio of these two lengths $Y/M=12.36826706\ldots$ is not an integer and most
-years should have 12 and leap years 13 months. In 432 BC, Athens astronomer Meton, discover that in
-19 years there are almost exactly 235 lunar months ($19\times 12.36826706=234.997$). This became a
-base for all calendar with lunar months and solar year.
-
-The Julian year has 365.25 days (on average), and the difference is $0.0078013 \linebreak[1]
-\mbox{days}=11'14''$ or 1 day in 128 years, while the Gregorian year has 365.2425 days, with the
-difference of $0.0003013 \mbox{ days} =26''$ or 1 day in 3319 years. More precise calendar will
-follow from the expansion of the length of the tropical year in an infinite fraction
-\[ {365.24219872}
-    =365+\dfrac{1}{4+\dfrac{1}{7+\dfrac{1}{1+\dfrac{1}{3+\dfrac{1}{5+\dfrac{1}{5+\cdots}}}}}}
-\]
-With the first fraction only, we have $365+\frac14=365.25$ days, what is Julian year. With the
-first two fraction, $365+\frac{1}{4+\frac{1}{7}}=365+\frac{7}{29}=365.2414$ and with the three
-$365+\frac{8}{33}=365.2424$ what is better then Gregorian year. With the four
-$365+\frac{31}{128}=365.2421875$ with the difference $0.0000112 \mbox{ days}=1''$ or 1 day in
-almost 10\,000 years. So, if in a cycle of 128 years we put 31 leap years, the calendar will be
-almost perfect.
-
-\subsection*{Brief History}
-
-In Babylon a calendar had 12 lunar months of 30 days each, with added extra month when necessary to
-keep the months in line with the seasons of the year. Later, a year of 354 days was introduced with
-12 months with intercalations in the years 3, 6, 8, 11, 14, 17, and 19 of the 19-year cycle. In
-Iran, Zoroastrian calendar has year of 12 months of 30 days, plus five days, giving totally 365.
-The ancient Egyptians measured the solar year as 365 days, divided into 12 months of 30 days each,
-with 5 extra days at the end. About 238~BC King Ptolemy~III added an extra day to every fourth
-year. In ancient Greece a lunar calendar was in use, with a year of 354 days. In Rome, the year had
-10 months with 304 days and began with March. Two more months, January and February were added
-later in the 7th century BC. Furthermore, an extra month had to be intercalated approximately every
-second year.
-
-In 45~BC Julius Caesar, upon the advice of the Alexandrian astronomer Sosigenes, decided to use a
-solar calendar similar to Egyptian. This calendar, known today the Julian calendar, had the normal
-year at 365 days, and the leap year, every fourth year, at 366 days. In this calendar January,
-March, May, July, September, and November had 31 days, other months 30 days, while February had 29
-or 30 days. This calendar also established the order of the months and the days of the week as they
-exist in present-day calendars. Julius Caesar also changed the name of the month Quintilis to
-Julius (July). In 8~AD the emperor Caesar Augustus renamed the month Sextilis to Augustus (August),
-increased it to 31 days, reduced September and November to 30 days, and increased October and
-December to 31 days. Such complicated calendar was adopted by Christian church and spread to western
-world.
-
-Since the year in Julian calendar was some longer then solar year, this discrepancy accumulated
-until by 1582 the error was 10 days. To fix it, Pope Gregory~XIII issued a decree dropping 10 days
-from the calendar and order that century years divisible by 400 should be leap years only. Catholic
-states adopted this new calendar immediately, but other counties did that later. Britain adopted it
-in 1752, Denmark and the Dutch and German Protestant states in 1699-1700, Soviet Union in 1918, and
-Greece in 1923. The monarch republic Holy Mountain, in Greece, is only territory with the official
-use of the Julian calendar, but some Orthodox churches also keep the Julian calendar for religious
-use.
-
-The Islamic calendar is a purely lunar. It has 12 lunar months alternately 30 and 29 days long. In
-each thirty years the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th, and 29th years have
-the last month as leap month with 30 instead of 29 days. So the year has 354 or 355 days. There are
-no intercalations of months and the months regress through all the seasons every $32\frac12$ years.
-
-The Jewish calendar is lunisolar, based on 12 lunar months of 29 days or 30 days. Such year has 354
-days, but an extra month of 30 days is intercalated in the 3rd, 6th, 8th, 11th, 14th, 17th, and
-19th years in a 19-year cycle. This gives an average length of 365.05 days.
-
-The Chinese calendar is also lunisolar, its year consisting of 12 months of alternately 29 and 30
-days, equal to 354 days. Intercalary months are inserting to keep the calendar year in step with
-the solar year of 365 days.
-
-\subsection*{Notices}
-
-These files may be freely used on any number of machines for any time period. It can be freely
-copied and distributed, on the condition that the distribution will be complete and with no
-modification.
-
-The author disclaims all warranties as to this software, whether express or implied, including
-without limitation any implied warranties of merchantability or fitness for a particular purpose.
-
-\subsection*{}
-\copyright Slobodan Jankovi\'c, \texttt{slobodan@archimed.filfak.ni.ac.yu}
-
-\end{document}
-
-
-
-\[ \frac{365.24219872}{29.530588} = 12.36826706\ldots
-    =12+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{16+\cfrac{1}{1+\dotsb}}}}}}}
-\]