\documentclass[green]{conditionechoblueshift}
\begin{document}
\name{\gResearch{}}

\bigquote{``To the scientist there is the joy in pursuing truth which
nearly counteracts the depressing revelations of truth.''}{--H.P. Lovecraft}

You are a Paranormal Researcher. Thanks to many years of rigorous 
schooling, you have the ability to do research in various labs around 
Dunwich. Labs are represented by packets on the wall. If you have 
a set of instructions giving you a project number, you may take the 
packet with that project number on it out of the packet on the wall. 
If you don't have instructions and a project number, you may not 
interact with the packet on the wall, even if you have this greensheet.

Some research is mechanicked by doing geometric constructions \footnote 
{Our thanks to Telmo and AHI for providing much of the text and all of 
the figures for this part of the greensheet.} with a compass and 
straightedge. Each packet will have one or several geometric figures 
that you must reconstruct in order to open it.

Research equipment is physrepped by a compass and a
straightedge.  The GMs will supply them, but you may bring your own.
You should also bring a pad of paper.  With your compass and
straightedge, you may:

\begin{itemz}
  \item Use the compass to draw arcs.
  \item Use the compass to mark off distances.
  \item Use the straightedge to make straight lines.
\end{itemz}

You may not:

\begin{itemz}
  \item Use your straightedge as a ruler.
  \item Use lined paper for your constructions.
  \item Guess an angle.
  \item Guess a distance or location.
\end{itemz}

In general, if you want to put the little pointy end of the compass
down on the paper, unless it's the first stroke of the figure, you
need to put it down on a pencil line or intersection.  Likewise, if
you want to draw a straight line, it's usually going to be a straight
line between two points.

Easy tasks should be straightforward from the examples below. More
difficult tasks may require some thinking and/or several steps. Most
geometric constructions can be solved in multiple ways, usually with a
trade-off between complexity of construction and thinking.

\subsubsection*{Elementary operations}

You should be able to do these very well.

Copying a segment: \nopagebreak

\includegraphics{\postscript/construction/copy-segment.eps}

Adding/subtracting segments:\nopagebreak

\includegraphics{\postscript/construction/add-segment.eps}

Copying an angle:\nopagebreak

\includegraphics{\postscript/construction/copy-angle.eps}

Adding/subtracting angles:\nopagebreak

\includegraphics{\postscript/construction/add-angle.eps}

Bisecting a segment/constructing a perpendicular line:\nopagebreak

\includegraphics{\postscript/construction/bisect-segment.eps}

Bisecting an angle:\nopagebreak

\includegraphics{\postscript/construction/bisect-angle.eps}

Angle of 60$^\circ$:\nopagebreak

\includegraphics{\postscript/construction/60-degrees.eps}

Other common angles include 30$^\circ$ (= 60$^\circ$/ 2) and
45$^\circ$ (= 90$^\circ$ / 2).

Line parallel to a line through a given point:\nopagebreak

\includegraphics{\postscript/construction/parallel.eps}

\pagebreak

\subsubsection*{Triangles}

You should be able to do these well.

Given 2 angles and a common side:\nopagebreak

\includegraphics{\postscript/construction/2-angles-common-side.eps}

Given 2 sides and a common angle:\nopagebreak

\includegraphics{\postscript/construction/2-sides-common-angle.eps}

Given 3 sides:\nopagebreak

\includegraphics{\postscript/construction/3-sides.eps}

Isosceles triangle (two sides / two angles of same size):\nopagebreak

\includegraphics{\postscript/construction/isosceles.eps}


\subsubsection*{Regular polygons}

You should be able to do these.\nopagebreak

\begin{tabular}{l@{\hspace{1in}}l}
Hexagon: & Pentagon: \\
\includegraphics[scale=0.8]{\postscript/construction/hexagon.eps}
&
\includegraphics[scale=0.5]{\postscript/construction/pentagon.eps}
\end{tabular}


\subsubsection*{Other operations}

You may want to understand these if you need to improvise.

Arc given chord and inscribed angle:\nopagebreak

\includegraphics{\postscript/construction/arc-chord-inscribed-angle.eps}

Circumcircle of a given triangle (for the center of a given circle,
just mark 3 points on it and use this):\nopagebreak

\includegraphics{\postscript/construction/circumcircle.eps}

Segment of size $\sqrt{a^2+b^2}$: build a rectangular triangle with
cathetus $a$ and $b$ and take the hypothenuse.

Segment of size $\sqrt{a^2+b^2}$: build a rectangular triangle with
cathetus $a$ and $b$ and take the hypothenuse.


\subsubsection*{Other triangles}

Constructions provided for informative purpose; you are not likely to
need these.

Given 2 sides and non-common angle (note that there are 2
solutions):\nopagebreak

\includegraphics{\postscript/construction/2-sides-other-angle.eps}

Given 2 angles and other side (note that there is a different solution
if you switch the sides):\nopagebreak

\includegraphics{\postscript/construction/2-angles-other-side.eps}


\end{document}
