Color Models as Tools in Teaching Mathematics

In this paper we discuss various situations how color models and patterns can be used to simplify the study of abstract mathematics and serve as tools in understanding mathematical ideas. We illustrate the realization of such models through the development of advanced computer technology. In particular, we present how a computer algebra software such as Mathematica, or a dynamic geometry environment, can be utilized to facilitate the study of transformation geometry and group theory

An Algorithm to Determine Non-Perfect Colorings that arise from Plane Crystallographic Groups

This paper presents a computer algorithm that assists us in our research on non-perfect colorings of plane crystallographic patterns

Weaving Mathematics

In this lecture, Dr. De las Peñas talks about the intersection of mathematics and Philippine indigenous weaving. Speaker: Ma. Louise Antonette N. De Las Peñas is a Professor at the Department of Mathematics and currently the Associate Dean for Research and Creative Work, Loyola Schools, Ateneo De Manila University, Philippines. Her research interests are discrete geometry, mathematical crystallography, group theory, and technology in mathematics education. She is a recipient of several research awards including the National Research Council of the Philippines (NRCP) Achievement Award in the Mathematical Sciences and the Philippine Commission on Higher Education Republica National Research Award. She has published her research extensively in international and national journals, book chapters, international conference publications; and a number of her published articles have been given recognition by the Philippine National Academy of Science and Technology (NAST) as outstanding scientific papers. Prof. De Las Peñas is an Executive Member of the International Union of Crystallography (IUCR) Mathematical and Theoretical Commission, and an International Program Committee Member of the Asian Technology Conference in Mathematics (ATCM). She is currently the column editor of The Mathematical Tourist of the journal The Mathematical Intelligencer and member of the Editorial Board of the Electronic Journal of Mathematics and Technology (EJMT).https://archium.ateneo.edu/magisterial-lectures/1030/thumbnail.jp

Tilings with Congruent Edge Coronae

In this paper, we discuss properties of a normal tiling of the Euclidean plane with congruent edge coronae. We prove that the congruence of the first edge coronae is enough to say that the tiling is isotoxal

The Use and Influence of Technology in Mathematics Education

The use of various types of technologies in the classroom and examinations is growing rapidly and is strongly influencing teaching and learning practices. In this paper, we will look at particular situations on how various technologies such as numerically capable calculators, graphics calculators, and technological tools that are CAS enabled or have CAS with Dynamic Geometry, impact students\u27 learning. We also discuss briefly the educational opportunities that are made available by the emergence of graphics calculators with capabilities of handling electronic learning activities, such as Casio’s Class Pad (see [1]) and Casio’s 9860 graphics calculator

Inspiring Students to Study and Learn Mathematics Using Technology

In this paper, we focus on the advantages of studying mathematics from analytical, graphical and geometric perspectives. Using Casio’s ClassPad 300 ([1]), we present activities on problems involving abstract concepts and real life applications. These activities viewed from the analytical, graphical, tabular and geometric points of view, promote creative ways to facilitate the learning of mathematics that inspire students with varying levels of ability. Consequently, students develop a profound appreciation and a deeper understanding of mathematics

Discovering New Tessellations Using Dynamic Geometry Software

In this paper we use dynamic geometry software to investigate a class of tilings called k-uniform tilings or tessellations. A tiling consisting of regular polygons whose vertices belong to k-transitivity classes under the action of its symmetry group (vertex-k-transitive) is said to be k-uniform. We also present constructions of tilings consisting of irregular polygons that are vertex-k-transitive

k -Isocoronal tilings

In this article, a framework is presented that allows the systematic derivation of planar edge-to-edge k-isocoronal tilings from tile-s-transitive tilings, s k. A tiling T is k-isocoronal if its vertex coronae form k orbits or k transitivity classes under the action of its symmetry group. The vertex corona of a vertex x of T is used to refer to the tiles that are incident to x. The k-isocoronal tilings include the vertex-k-transitive tilings (k-isogonal) and k-uniform tilings. In a vertex-k- transitive tiling, the vertices form k transitivity classes under its symmetry group. If this tiling consists of regular polygons then it is k-uniform. This article also presents the classification of isocoronal tilings in the Euclidean plane

Mathematical and Anthropological Analysis of Northern Luzon Funeral Textile

The study presents a mathematical analysis and provides an anthropological perspective of the funeral textile of the indigenous communities in northern Luzon, Philippines. In particular, a symmetry analysis is performed, based on principles of group theory and transformation geometry, on the various repeating patterns found in funeral garments and blankets. Results show that particular frieze groups and plane crystallographic groups are favored due to choice of motifs which are reflective of cultural beliefs and funeral traditions, as well as weaving style and methodology. The results of the analysis point to the depth of mathematics present in the work of the weaver, who is able to arrive at meaningful geometric designs without formal training in mathematics. This study contributes directly to the branch of mathematics pertaining to mathematical crystallography in art and cultural heritage which deals, among others, with the use of group theoretic methods and tools in mathematical crystallography to understand the mathematics in artworks arising from various cultures all over the world. It provides further data and analysis to the growing body of literature that uses symmetry to enhance interpretation of culture from the artistic style of its artifacts