$$ \huge \sqrt{2} + \sqrt{3} \;\approx\; \pi $$
$$\large \begin{align}
\sqrt{2} + \sqrt{3} &= |\overline{AB}| + |\overline{CD}| \\
&= |\widehat{AB^\prime}| + |\widehat{CD^\prime}| \\
&\approx |\stackrel{\frown}{AB^\prime}| + |\stackrel{\frown}{CD^\prime}| \\
&\approx |\stackrel{\frown}{AC}| \\[6pt]
&= \pi
\end{align}$$