Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new characterization of Möbius transformations by use of Apollonius hexagons


Authors: Hiroshi Haruki and Themistocles M. Rassias
Journal: Proc. Amer. Math. Soc. 128 (2000), 2105-2109
MSC (1991): Primary 39B40; Secondary 33A70
Published electronically: February 25, 2000
MathSciNet review: 1653398
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to give a new characterization of Möbius transformations from the standpoint of conformal mappings. To this end a new concept of Apollonius hexagons on the complex plane is used.


References [Enhancements On Off] (What's this?)

  • 1. H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited, Random House, New York, 1967.
  • 2. B. A. Fuchs and B. V. Shabat, Functions of a complex variable and some of their applications. Vol. I, Original translation by J. Berry; revised and expanded by J. W. Reed, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass., 1964. MR 0160878 (28 #4087)
  • 3. H. Haruki and Th. M. Rassias, A new characteristic of Möbius transformations by use of Apollonius quadrilaterals, Proc. Amer. Math. Soc. 126 (10) (1998), 2857-2861. CMP 99:04
  • 4. Hiroshi Haruki, A proof of the principle of circle-transformation by the use of a theorem on univalent functions, Enseignement Math. (2) 18 (1972), 145–146. MR 0325966 (48 #4312)
  • 5. S. Rabinowitz (ed.), Index to Mathematical Problems 1980-1984, MathPro Press, 1992.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 39B40, 33A70

Retrieve articles in all journals with MSC (1991): 39B40, 33A70


Additional Information

Hiroshi Haruki
Affiliation: Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Themistocles M. Rassias
Affiliation: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece
Email: trassias@math.ntua.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05246-1
PII: S 0002-9939(00)05246-1
Keywords: M\"obius transformations, conformal mapping, Apollonius hexagons
Published electronically: February 25, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society