On the reflection principle and some elementary ratios of conformal radii (Q1059172)

By very clever use of reflection methods and the introduction of the angular conformal radius of an \(\alpha\)-trilateral, the conformal radii of a large number of regions are explicitly given. For example, if Q is the unit square, \(z_ 0\) its center, and G is the L-shaped region obtained by reflecting Q to the right and above, the conformal radius r(G) of G with respect to \(z_ 0\) is \(\tau\) \(\cdot r(Q)\) with \(\tau =3(1-t^{2/3}+t^{4/3})/(1+t^{2/3}+t^{4/3})\) with \(t=\sqrt{2}-1\), i.e. \(\tau\) \(\sim 1.21179\).