To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Studying Non-Euclidean Tilings and Their Groups with the Aid of Technology

Ma. Louise Antonette De Las Penas

Glenn Laigo

Eden Delight Provido
Ateneo de Manila University


In recent years, the opportunities to explore the non-Euclidean planes and visualize the various mathematical properties that are satisfied in these planes have been made available to teachers, students and researchers with the presence of technology. In this work, the technological approaches that have facilitated our research on non-Euclidean tilings and their groups will be discussed. The first part of the paper will focus on the method in determining the symmetry groups of semi-regular tilings on the hyperbolic and spherical planes where investigations were carried out using the L2Primitive/Tess packages of Mathematica. In the second part of the paper, an approach in coloring hyperbolic semi-regular tilings will be presented using, as tools, the GAP and the Coloring the Hyperbolic Plane (CHP) programs. Moreover, discussion will also be given on the use of the CHP program in providing some characterizations of the subgroups of Hyperbolic Triangle groups - conjugates, normalizers, etc.

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