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\centerline{MONT 109N -- Mathematics Across Cultures}
\centerline{Problem Set 2 -- Mayan calendar calculations}
\centerline{Due: Friday, February 18}
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\noindent
{\it Note:}  You may check your work on these questions using
the Mayan Calendar Converter link on the course homepage.  But, 
you must show enough details to justify your answer completely
to get full credit on these questions.
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\noindent
A.  In the Mayan Calendar Round, as I am writing this 
problem set on Tuesday, February 8, today is {\it 11 Eznab 11 Pax}.  
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\item{1)}  What will the Calendar Round date be on the 
day this assignment is due:  Friday, February 18, 2011?  (Justify your answer using modular
arithmetic calculations.)
\item{2)}  What will the Calendar Round date be on 
Saturday, February 18, 2012?  (Justify your answer using modular
arithmetic calculations.)
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\noindent
B.  The {\it Leiden Plaque} is a carved jadeite ornament
from the early Classic period that shows 
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\item{$\bullet$} on the front, an elaborately costumed king standing
on a captive (soon to be a sacrificial victim, apparently!) 
\item{$\bullet$} an inscribed Long Count
date on the rear.
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\noindent  
The plaque is thought to be a record of the start of the reign of one 
of the kings of the city of Tikal in the Mayan heartland.
There is a link to a hand-drawn reproduction
of the date on the course home page.  
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\item{1)}  Look it up there
and decipher the date (the numbers of baktuns, 
katuns, tuns, uinals, days since the starting date of 
the current Great Cycle.  Note: these numbers always appear
after a large ``Initial Series Introduction Glyph''
at the top, and are read in the order given above, top
to bottom.  Express your answer as a date in the form
{\it baktuns.katuns.tuns.uinals.days}, and as a total number
of days since the start of the current Great Cycle.  (If your translation
is correct, the Calendar Round date on the day recorded
should be {\it 1 Eb 20 Xul} or {\it 1 Eb 0 Yaxkin}, using
the Mayans' convention that the 20th day of a month is the ``seating''
of the next month, written as 0). 
\item{2)}  Give a rough estimate of the date of the plaque in {\it our
calendar system}, using the standard start date of the Long Count
in the year 3114 BCE.   {\it Note:  This is one of the
earliest known Long Count dates that has survived}.
\item{3)}  (Extra Credit)  If you look carefully, you 
can see the Calendar Round date {\it 1 Eb 0 Yaxkin} on
the Leiden plaque inscription too.  Where are the 
corresponding glyphs on the plaque?  Note:  The glyphs for
the Sacred Round and Vague Year ``months'' are reproduced
in lots of places on line.   
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\noindent
C.  February 8, 2011 corresponds to the Long Count 
date 12.19.18.1.18.  Recall that there are 20 days in
a uinal, 18 uinals in a tun, 20 tuns in a katun, and
20 katuns in a baktun.  The completion of the current
Great Cycle (when the Long Count date reaches 13.0.0.0.0)
is coming up quite soon(!)  On what date (month, day, year) 
in our calendar will this occur?    
\bye 
