Squaring rectangles for dumbbells
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- by J. W. Cannon, W. J. Floyd and W. R. Parry
- Conform. Geom. Dyn. 12 (2008), 109-132
- DOI: https://doi.org/10.1090/S1088-4173-08-00182-3
- Published electronically: August 14, 2008
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Abstract:
The theorem on squaring a rectangle (see Schramm [Israel J. Math. 84 (1993)] and Cannon-Floyd-Parry [Contemp. Math. 169, AMS, 1994]) 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 Riemann mapping.References
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Bibliographic Information
- J. W. Cannon
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- Email: cannon@math.byu.edu
- W. J. Floyd
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
- MR Author ID: 67750
- Email: floyd@math.vt.edu
- W. R. Parry
- Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
- MR Author ID: 136390
- Email: walter.parry@emich.edu
- Received by editor(s): June 19, 2008
- Published electronically: August 14, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Conform. Geom. Dyn. 12 (2008), 109-132
- MSC (2000): Primary 52C20, 52C26
- DOI: https://doi.org/10.1090/S1088-4173-08-00182-3
- MathSciNet review: 2434355