• School Mathematics
• /
• v.15 no.4
• /
• pp.957-973
• /
• 2013

This study analyzed Secondary Mathematically Gifted' mathematical thinking processes demonstrated from the activities. They configured regular triangle tessellations in the Non-Euclidean hyperbolic disk model. The students constructed the figure and transformation to construct the tessellation in the poincare disk. gsp file which is the dynamic geometric environmen, The students were to explore the characteristics of the hyperbolic segments, construct an equilateral triangle and inversion. In this process, a variety of strategic thinking process appeared and they recognized to the Non-Euclidean geometric system.

• The KIPS Transactions:PartA
• /
• v.8A no.4
• /
• pp.489-498
• /
• 2001

A new method for local control of arbitrary scattered data interpolation in the hyperbolic plane is developed in this paper. The issue associated with local control is very critical in the interactive in the interactive design field. Especially the suggested method in this paper could be effectively applied to the interactive shape modeling of genus-N objects, which are constructed on the hyperbolic plane. Since the effects of the changed data affects only the limited area around itself, it is more convenient for end-users to design a genus-N object interactively. Therefore, by improving the global interpolation on the hyperbolic plane where the genus-N object is constructed, this research is aiming at the development and implementation of the local interpolation on the hyperbolic plane. It is implemented using the following process. First, for localizing the interpolating functions, the hyperbolic domain is tessellated into arbitrary triangle patches and the group of adjacent triangle patches of each data point is defined as a sub-domain. On each sub-domain, a weight function is defined. Last, by blending of three weight functions on the overlapped triangles, local MQ interpolation is completed. Consequently, it is compared with the global MQ interpolation using several sample data and functions.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.823-833
• /
• 2009

It is well-known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of the modular group, then its translates by the group elements form a locally finite tessellation and its side-pairing transformations form a system of generators for the group. Such hyperbolically convex polygons can be obtained by using Dirichlet's and Ford's polygon constructions. Another method of obtaining a fundamental domain for subgroups of the modular group is through the use of a right coset decomposition and we call such domains standard fundamental domains. In this paper we give subgroups of the modular group which do not have hyperbolically convex standard fundamental domain containing only inequivalent cusps.