## Squaring rectangles for dumbbells

###
J. W. Cannon, W. J. Floyd, and W. R. Parry

June 17, 2008

### Abstract

The theorem on squaring a rectangle (see Schramm
(*Squaring tilings with prescribed combinatorics*,
Israel J. Math. **84** (1993), 97--118) and
Cannon-Floyd-Parry (*Squaring rectangles: the finite
Riemann mapping theorem*)) gives a combinatorial version of
the Riemann mapping theorem. We elucidate by example (the dumbbell)
some of the limitations of rectangle-squaring as an approximation to
the classical Riemamnn mapping.
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