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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A plot of the circle of curvature $\{ x = (x_{1},x_{2}) \in {\@mathbb {R}}^{2}: \delimiter "026A30C x - (0,\frac  {1}{2}) \delimiter "026A30C = \frac  {1}{2} \}$ of $x_{2}=x_{1}^2$ at $x_{1} = 0$. (Problem 60.9)}}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A plot of the function $x_{2}=x_{1}^3$. The curvature $\kappa (x_{1}) = \frac  {6x_{1}}{(1 + 9x_{1}^{4})^{\frac  {3}{2}}}$ changes sign at the inflection point $x = (x_{1},x_{2}) = (0,0)$. It is negative for $x_{1} < 0$ and positive for $x_{1} > 0$. (Problem 60.12 (b))}}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces A plot of the hanging chain described by the function $y(x) = c \qopname  \relax o{cosh}(\frac  {x}{c})$ (with $c = \frac  {1}{2}$). Force equilibrium for the part of the chain between $0$ and $x$ requires that $T(0) = T(x) \qopname  \relax o{cos}\psi $ (horizontal equilibrium) and $\rho g s(x) = T(x) \qopname  \relax o{sin}\psi $ (vertical equilibrium). (Problem 60.13)}}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces A plot of the relation between small changes $\bigtriangleup \rho $ and $\bigtriangleup \theta $ in $\rho $ and $\theta $, and the corresponding change in position $\bigtriangleup s$. From the figure and old Pythagoras we get $(\bigtriangleup s)^{2} \approx \rho ^{2} (\bigtriangleup \theta )^{2} + (\bigtriangleup \rho )^{2}$, which in the infinitesimal limit turns into $ds^{2} = \rho ^{2} d\theta ^{2} + d\rho ^{2}$. (Problem 60.15)}}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces A plot of the surface $S$, a parallelogram spanned by the vectors $(1,0,1)$ and $(0,1,2)$. (Problem 62.6)}}{11}}
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