% Math 370 hw7 Spring 2014
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\title{History of Mathematics \\
Homework 7
}
\author{Ethan Bolker}

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Due Thursday, April 17

\begin{enumerate}

\item
Turn in a serious progress report on your term paper. 

Some of these questions might help you think about where you are:

\begin{itemize}

\item What particular mathematics will you discuss? What part of its
history?
\item How will you balance modern and historical exposition and notation?

\item How far along are  you? 
\item What is left to do? 
\item What's your plan for finishing? 
\item What sources have you found? 
\item What sources are still missing? 
\end{itemize}


The form of your report is up to you - it might be a detailed outline,
or rough drafts of some of the parts. But of course it's in \LaTeX{}.

Since you're still doing the work, its perfectly OK for you to report
that you don't yet have answers to the questions you're asking. You
need to show progress, not results (yet).

\item Show that in Figure~3.5 in the text the point $B$ constructed by
  making $DB$ parallel to the axis of the parabola $AK$ is the
  furthest point from the chord $AC$. (Modern tools are OK.)

\item Show that in Figure~3.3 $\Delta PQq = 8 \Delta PRQ$.

\item Show that in Figure~3.5 $EB = BD$ given that $CF$ is tangent to
the parabola.

\item The angle bisectors of a triangle meet at the \emph{incenter}:
  the center of the circle inscribed in the triangle. The
  perpendicular bisectors of the sides meet at the
  \emph{circumcenter}: the center of the circle in which the triangle
  is inscribed. The medians meet at the \emph{centroid}: the center of
  gravity.

What is the geometric significance of the point at which the altitudes
of a triangle meet? 

\end{enumerate}

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