<P>

A complicated and accurate calendar using three simultaneous independent systems. It consisted of the Long Count,
Tzolkin, and Haab. The Long Count is related to <a href="PrecessionoftheEquinoxes.html">precession of the equinoxes</a>, and will end in 2012 when the
<a href="WinterSolstice.html">winter solstice</a> will be very near the point at which the ecliptic plane and galactic plane intercept (Jenkins).

<P>
The Long Count is a mixed base 20/base 18 representation of the number of days since the beginning of the &quot;Mayan Era.&quot;
The starting point is written as 13.0.0.0.0, which corresponds to Aug 13 3114 <a href="BC.html">BC</a>, Aug 11 3114 <a href="BC.html">BC</a>, or Oct 15
3374 <a href="BC.html">BC</a> <a href="GregorianCalendar.html">Gregorian</a> (according to different authorities). Mayan dates are written in
the form baktun.katun.tun.unial.kin, where these lengths are defined below.

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="LEFT">Unit</TD>
<TD ALIGN="LEFT">Definition</TD>
<TD ALIGN="LEFT">Days</TD>
<TD ALIGN="LEFT">Years</TD>
</TR>
<TR><TD ALIGN="LEFT">unial</TD>
<TD ALIGN="LEFT">20 kin</TD>
<TD ALIGN="LEFT">20 days</TD>
<TD ALIGN="LEFT">--</TD>
</TR>
<TR><TD ALIGN="LEFT">tun</TD>
<TD ALIGN="LEFT">18 unial</TD>
<TD ALIGN="LEFT">360 days</TD>
<TD ALIGN="LEFT"><IMG
WIDTH="29" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="http://scienceworld.wolfram.com/astronomy/mimg13.gif"> year</TD>
</TR>
<TR><TD ALIGN="LEFT">katun</TD>
<TD ALIGN="LEFT">20 tun</TD>
<TD ALIGN="LEFT">7,200 days</TD>
<TD ALIGN="LEFT"><IMG
WIDTH="37" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="http://scienceworld.wolfram.com/astronomy/mimg14.gif"> years</TD>
</TR>
<TR><TD ALIGN="LEFT">baktun</TD>
<TD ALIGN="LEFT">20 katun</TD>
<TD ALIGN="LEFT">144,000 days</TD>
<TD ALIGN="LEFT"><IMG
WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="http://scienceworld.wolfram.com/astronomy/mimg15.gif"> years</TD>
</TR>
</TABLE>
</DIV>

<P>
The Tzolkin was a combination of a numbered &quot;week&quot; of 13 days and a named &quot;week&quot; of 20 days.

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="RIGHT">0</TD>
<TD ALIGN="LEFT">Ahau</TD>
<TD ALIGN="RIGHT">5</TD>
<TD ALIGN="LEFT">Chicchan</TD>
<TD ALIGN="RIGHT">10</TD>
<TD ALIGN="LEFT">Oc</TD>
<TD ALIGN="RIGHT">15</TD>
<TD ALIGN="LEFT">Men</TD>
</TR>
<TR><TD ALIGN="RIGHT">1</TD>
<TD ALIGN="LEFT">Imix</TD>
<TD ALIGN="RIGHT">6</TD>
<TD ALIGN="LEFT">Cimi</TD>
<TD ALIGN="RIGHT">11</TD>
<TD ALIGN="LEFT">Chuen</TD>
<TD ALIGN="RIGHT">16</TD>
<TD ALIGN="LEFT">Cib</TD>
</TR>
<TR><TD ALIGN="RIGHT">2</TD>
<TD ALIGN="LEFT">Ik</TD>
<TD ALIGN="RIGHT">7</TD>
<TD ALIGN="LEFT">Manik</TD>
<TD ALIGN="RIGHT">12</TD>
<TD ALIGN="LEFT">Eb</TD>
<TD ALIGN="RIGHT">17</TD>
<TD ALIGN="LEFT">Caban</TD>
</TR>
<TR><TD ALIGN="RIGHT">3</TD>
<TD ALIGN="LEFT">Akbal</TD>
<TD ALIGN="RIGHT">8</TD>
<TD ALIGN="LEFT">Lamat</TD>
<TD ALIGN="RIGHT">13</TD>
<TD ALIGN="LEFT">Ben</TD>
<TD ALIGN="RIGHT">18</TD>
<TD ALIGN="LEFT">Etznab</TD>
</TR>
<TR><TD ALIGN="RIGHT">4</TD>
<TD ALIGN="LEFT">Kan</TD>
<TD ALIGN="RIGHT">9</TD>
<TD ALIGN="LEFT">Muluc</TD>
<TD ALIGN="RIGHT">14</TD>
<TD ALIGN="LEFT">Ix</TD>
<TD ALIGN="RIGHT">19</TD>
<TD ALIGN="LEFT">Caunac</TD>
</TR>
</TABLE>
</DIV>

<P>
The Haab was a civil calendar consisting of 18 &quot;months&quot; of 20 days each (numbered 0-19), followed by 5 extra days (called
Uayeb and observed as days of prayer and mourning), giving total year length of 365 days.

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="RIGHT">1</TD>
<TD ALIGN="LEFT">Pop</TD>
<TD ALIGN="RIGHT">7</TD>
<TD ALIGN="LEFT">Yaxkin</TD>
<TD ALIGN="RIGHT">13</TD>
<TD ALIGN="LEFT">Mac</TD>
</TR>
<TR><TD ALIGN="RIGHT">2</TD>
<TD ALIGN="LEFT">Uo</TD>
<TD ALIGN="RIGHT">8</TD>
<TD ALIGN="LEFT">Mol</TD>
<TD ALIGN="RIGHT">14</TD>
<TD ALIGN="LEFT">Kankin</TD>
</TR>
<TR><TD ALIGN="RIGHT">3</TD>
<TD ALIGN="LEFT">Zip</TD>
<TD ALIGN="RIGHT">9</TD>
<TD ALIGN="LEFT">Chen</TD>
<TD ALIGN="RIGHT">15</TD>
<TD ALIGN="LEFT">Muan</TD>
</TR>
<TR><TD ALIGN="RIGHT">4</TD>
<TD ALIGN="LEFT">Zotz</TD>
<TD ALIGN="RIGHT">10</TD>
<TD ALIGN="LEFT">Yax</TD>
<TD ALIGN="RIGHT">16</TD>
<TD ALIGN="LEFT">Pax</TD>
</TR>
<TR><TD ALIGN="RIGHT">5</TD>
<TD ALIGN="LEFT">Tzec</TD>
<TD ALIGN="RIGHT">11</TD>
<TD ALIGN="LEFT">Zac</TD>
<TD ALIGN="RIGHT">17</TD>
<TD ALIGN="LEFT">Kayab</TD>
</TR>
<TR><TD ALIGN="RIGHT">6</TD>
<TD ALIGN="LEFT">Xul</TD>
<TD ALIGN="RIGHT">12</TD>
<TD ALIGN="LEFT">Ceh</TD>
<TD ALIGN="RIGHT">18</TD>
<TD ALIGN="LEFT">Cumku</TD>
</TR>
</TABLE>
</DIV>

<P>
For example, my birthday (March 18, 1969 <a href="AD.html">AD</a> <a href="GregorianCalendar.html">Gregorian</a>) would be written
12.17.15.10.14, 8 Muluc 17 Kayab.

<P>
The Mayan calendar was adopted by other central American cultures including Aztecs and Toltec. Mayans were aware that the
year was slightly longer than 365 days, and computed the <a href="TropicalYear.html">tropical year</a> as 365.242036 days.