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Name (Last, First): $\underline{\hspace{3in}}$ \hfill Student ID: $\underline{\hspace{2in}}$

\vskip 2mm

{\small
  \href{\myurl}{Dror Bar-Natan}:
  \href{\myurl/classes/}{Classes}:
  \href{\myurl/classes/\#1415}{2014-15}:
  \href{\myurl/classes/15-475-ProblemSolving}{MAT 475 Problem Solving Seminar}:
  \hfill\url{http://drorbn.net/15-475}
}

\vskip 3mm

{\large\bf Quiz 6} Around the Isoperimetric Inequality, February 24, 2015. You have 25 minutes to solve the problem below. Please write on both sides of the page. \hfill {\bf Good Luck!}

\vskip 2mm

\noindent{\bf Problem} (the two parts are of equal value).
\begin{itemize}
\item Of all the parallelograms of area 1, which one has the least perimeter?
\item Of all the parallelepipeds of volume 1, which has the smallest surface area?
\end{itemize}
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\vskip -9mm
\noindent{\bf Extra Problem} (no credit). If you are bored, think about the following; we will talk about it in class later: Let an angle $\alpha$ be given, and consider triangles $ABC$ with internal angle $\alpha$ near $A$ and side lengths $AB=c$, $AC=b$, and $BC=c$. Of all such triangles with a fixed value for $a-(b+c)$, which one has the least area?
\begin{itemize}
\item Solve the problem.
\item Why am I asking it?
\end{itemize}

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