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\title{HW3 \\
5500 Spring 2012}
\author{Andrej Cherkaev}
\date{}
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\item  Assume that Dido and her people land on a circular island, its diameter is equal to $R$. Solve Dido problem at a shore of that island, assuming that the length of the rope is smaller than $2\,R$. 

\item  A heavy chain of the length $L=4$ is hanged over a floor $h=0$, a part of the chain lies on a floor. The coordinates of the supports are $h=1, x=0$ and $h=1, x=1$. Find a position of equilibrium of the chain. 

\item  Derive equations for geodesics on a circular cone $z= a\, r$, where $z$ and $r$ are cylindrical coordinates, and $a$ is a positive real parameter. Find a distance between points $(r=1, z=a, \theta =0)$ and $(r=2, z=2 a, \theta =\pi)$. Use cylindrical coordinates. 
\end{enumerate}

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