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AN APPLICATION OF TILINGS IN THE HYPERBOLIC PLANE
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  • Journal title : Honam Mathematical Journal
  • Volume 29, Issue 3,  2007, pp.481-493
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2007.29.3.481
 Title & Authors
AN APPLICATION OF TILINGS IN THE HYPERBOLIC PLANE
Park, Jong-Youll;
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 Abstract
We will construct several types of semi-regular tilings of a hyperbolic unit disk model by defining geometric features of the definition of distance in a hyperbolic plane, area of triangle, and isometry of inversions. We researched the method of regular tilings and semi-regular tilings of hyperbolic unit disk model and wrote an semi-regular tiling construction algorithm using Cabri2 program and Cinderella program. Lastly, We want to make a product related to traditional heritage cultural patterns using Photoshop, so we'll model the advertising photos of cites; Seoul, Gwangju.
 Keywords
Regular tiling;Semi-regular tiling;Hyperbolic unit disk model;Cabri program;Cinderella program;
 Language
English
 Cited by
 References
1.
Saul Stahl, The Poincare Half-Plane, A Gateway to Modern Geometry, Jones and Bartlett Pub. 1993.

2.
Arlan Ramsay and Robert D. Richtmyer, Introduction to Hyperbolic Geometry, Springer, 1995.

3.
Dan Gremillion and Michael Keyton(translated by Ryoo and Jang), Cabri Geometry Guidebook(Korean version), Texas Instrument, 1997.

4.
James W.Anderson, Hyperbolic Geometry, 2th, Springer UMS, 2000

5.
Interactive Geometry Cinderella 2003.

6.
http://aleph0.clarku.edu/ djoyce/poincare/poincare.html.

7.
http://windshoes.new21.org/art-escher.htm.