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\markright{MATH 110 -- Mathematics Through Time, Midterm Exam}

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\begin{document}

\noindent
Your Name:  $\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$ 

\vskip 10pt
\noindent
{\it Directions}
\vskip 10pt
Do all work on the sheets provided (if you use the back of a sheet,
please place a note telling me to look there).  
There is an extra sheet of scratch paper at the end.  You may 
detach that if you like, but please hand it in with your exam.

Please do not write below.
\vskip 30pt
\begin{center}
\begin{tabular}{|l||r|}
\hline
Problem & Points/Poss    \Strut \\
\hline\hline
I  & \hfil/\  15\hfil \Strut \\
\hline
II  & \hfil/\  30\hfil \Strut \\
\hline
III  & \hfil/\  20\hfil \Strut \\
\hline
IV  & \hfil/\  10\hfil \Strut \\
\hline
V (Essay)  & \hfil/\  25\hfil \Strut \\
\hline\hline
Total   & \hfil/100\hfil \Strut \\
\hline
\end{tabular}
\end{center}
\vfill\eject
\noindent
I.  Short answer.  Answer any 6 of the following.  
\vskip 10pt
\begin{enumerate}
\item[A)] (2.5)  What base 10 number is represented by these Egyptian
hieroglyphs? 
\vglue 1.0truein
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vskip 10pt
\item[B)] (2.5)  What base 10 number is represented in the
Babylonian way by these symbols?
\vglue 1.0truein
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vskip 10pt
\item[C)] (2.5)  Approximately {\it when} was the Middle Kingdom period in 
Egyptian history?
\vskip 10pt
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vskip 10pt
\item[D)] (2.5)  The name for the writing system used in question B is
\vskip 10pt
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vskip 10pt
\item[E)] (2.5)  What are the two most important surviving records of ancient Egyptian 
mathematics?
\vskip 10pt
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vskip 10pt
\item[F)] (2.5)  Most of the geographical area of the Old Babylonian 
kingdoms is contained in what present-day country?
\vskip 10pt
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vskip 10pt
\item[G)] (2.5)  Approximately when did Thales live and what part of the Greek 
world did he come from?  
\vskip 10pt
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}  
\vskip 10pt
\item[H)] (2.5)  Who founded the Academy in Athens whose entryway was inscribed ``let no one unversed in 
geometry enter here?''
\vskip 10pt
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\end{enumerate}
\vfill\eject
\noindent
II.  Compute ``in the Egyptian way"
\begin{enumerate}
\item[A)] (15) $37 \times 136$
\vglue 3.0truein

\item{B)} (15) $52 \div 18$  (``compute with $18$ until you find $52$'')
\end{enumerate}
\vfill\eject
\noindent
III. (20) An Old Babylonian problem text asks for the side of a square
if the area of the square minus the side is the base
60 number $14,30;0$.  The tablet says to do this to 
solve the problem (all numbers in base 60, of course!):
``Take half of 1, which is $0;30$, square that
to get $0;15$, add the $14,30$ to get 
$14,30;15$.  The last number is the square of
$29;30$.  Now add the $0;30$ to get $30$, which
is the side of the square.''
\vskip 10pt
In modern language, the problem is to solve for $x$ if $x^2 - x - 870 = 0$.  
Find $x$ by solving this equation, then explain how the Babylonian method of solution
is essentially the same as using the quadratic formula for the
equation $x^2 - x - 870 = 0$.  
\vfill\eject
\noindent
IV.  (10) What is Proposition 1 in Euclid's {\it Elements}?  Describe the 
associated construction.   
\vfill
\eject
\noindent
IV.  Essay.  (25) ``The distinguishing feature of Babylonian mathematics is
its algebraic character.''  Of the historians we have mentioned, who
would agree with this claim, and who would disagree?  
Explain using the the interpretations your historians would give 
for the YBC 6967 problem of solving the equation $x = 60/x + 7$.
\vfill\eject

\end{document}
