\magnification=\magstep1
\leftline{MONT 108N -- Mathematics Through Time}
\leftline{Makeup Midterm Exam, November 3, 2010}
\leftline{Your Name:  $\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$ }
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\noindent
{\it Directions}
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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.
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\noindent
I.  Compute ``the Egyptian way"
\medskip
\item{A)} (10) $51 \times 187$
\vglue 3.0truein.

\item{B)} (10) $1332 \div 47$ (find the quotient and the remainder)
\vfill\eject
\noindent
II.  
\item{A)} (10) Express the base 8 number $(246)_8$ in base 10.
\vglue 4.0truein
\item{B)} (10) Express the base 2 number $(111000111)_2$ in base 60.
\vfill\eject
\noindent
III.  A Babylonian problem text asks for the side of a square
if the area of the square minus the side is the base
60 number $(14:30)_{60}$.  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.''
\medskip
\item{A)} (15) Solve this problem using modern methods.
\vglue 4.0truein
\item{B)}  (5)  Explain how the Babylonian method of solution
is essentially the same as using the quadratic formula for an
equation of the form $x^2 - px = q$.  
\vfill\eject
\noindent
IV.  Short answer:
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\item{A)} (2.5)  What base 10 number is represented by these Egyptian
hieroglyphs? 
\vglue 1.0truein
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\bigskip
\item{B)} (2.5)  What base 10 number is represented in the
Babylonian way by these symbols?
\vglue 1.0truein
\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
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\item{C)} (2.5)  Approximately {\it when} was the Old Babylonian period in 
Mesopotamian history?
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\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
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\item{D)} (2.5)  The name for the writing system used in part B is
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\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
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\item{E)} (2.5)  What are the surviving records of Egyptian mathematics?
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\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
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\item{F)} (2.5)  Most of the geographical area of the Old Babylonian 
kingdoms is contained in what present-day country?
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\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
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\item{G)} (2.5)  What was special about the Egyptian way of 
dealing with fractions? 
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\leftline{Answer: 
$\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}  
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\item{H)} (2.5)  Which Old Babylonian tablet apparently contains
a table of Pythagorean triples?
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\leftline{Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}
\vfill
\eject
\noindent
V.  Essay.  (20) ``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
$\qquad$
\bye
