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Articles 1 - 8 of 8
Full-Text Articles in Geometry and Topology
(A,B,C) Tilings With Prescribed Symmetry Groups From Regular Triangle Or Hexagon Tiling, Mark D. Tomenes, Ma. Louise Antonette N. De Las Penas
(A,B,C) Tilings With Prescribed Symmetry Groups From Regular Triangle Or Hexagon Tiling, Mark D. Tomenes, Ma. Louise Antonette N. De Las Penas
Mathematics Faculty Publications
A tiling T of the Euclidean plane (E2) is a countable collection of closed topological disks called tiles T = {Ti : i ∈ N} that is a covering (Ui Ti = E2) as well as a packing (Int(Ti) ∩ Int(Tj) = ∅ if i ̸= j, Int(T) denotes the interior of tile T). One of the problems of interest in discrete geometry is the classification of tilings based on transitivity properties of their vertices, edges and tiles. This talk presents a family of tilings whose vertices, edges and tiles have exactly a, b and c orbits, respectively, under the …
Differentiated Instruction In Geometry Using Low Floor, High Ceiling Mathematical Tasks, Franklin R. Falculan, Maria Alva Q. Aberin
Differentiated Instruction In Geometry Using Low Floor, High Ceiling Mathematical Tasks, Franklin R. Falculan, Maria Alva Q. Aberin
Mathematics Faculty Publications
This study investigated the effects of using Low Floor High Ceiling (LFHC) mathematical tasks on students’ conceptual understanding and procedural fluency in seventh-grade Geometry by closely examining pre-test and posttest results. Two intact classes composed of thirty-two grade 7 students in each class participated in the study. The control group was taught and had practice using conventional, algorithmic tasks while the experimental group was taught and had practice using LFHC mathematical tasks. Data analysis revealed that, as compared to students exposed to algorithmic problems, students exposed to LFHC activities were much more mathematically proficient in Geometry, at the very least …
Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola
Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola
Mathematics Faculty Publications
No abstract provided.
Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas
Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas
Mathematics Faculty Publications
A geometric realization of an abstract polyhedron P is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Gamma. The method entails finding a real orthogonal representation of Gamma of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.
K -Isocoronal Tilings, Eduard C. Taganap, Ma. Louise Antonette N. De Las Peñas
K -Isocoronal Tilings, Eduard C. Taganap, Ma. Louise Antonette N. De Las Peñas
Mathematics Faculty Publications
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 …
Primitive Substitution Tilings With Rotational Symmetries, April Lynne D. Say-Awen, Ma. Louise Antonette N. De Las Peñas, Dirk Frettlöh
Primitive Substitution Tilings With Rotational Symmetries, April Lynne D. Say-Awen, Ma. Louise Antonette N. De Las Peñas, Dirk Frettlöh
Mathematics Faculty Publications
This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six- and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.
Construction Of Weavings In The Plane, Eden Delight Miro, Aliw-Iw Zambrano, Agnes Garciano
Construction Of Weavings In The Plane, Eden Delight Miro, Aliw-Iw Zambrano, Agnes Garciano
Mathematics Faculty Publications
This work develops, in graph-theoretic terms, a methodology for systematically constructing weavings of overlapping nets derived from 2-colorings of the plane. From a 2-coloring, two disjoint simple, connected graphs called nets are constructed. The union of these nets forms an overlapping net, and a weaving map is defined on the intersection points of the overlapping net to form a weaving. Furthermore, a procedure is given for the construction of mixed overlapping nets and for deriving weavings from them.
On Color Fixing Groups Associated With Colored Symmetrical Tilings, April Lynne D. Say-Awen, Ma. Louise Antonette N. De Las Peñas, Teofina A. Rapanut
On Color Fixing Groups Associated With Colored Symmetrical Tilings, April Lynne D. Say-Awen, Ma. Louise Antonette N. De Las Peñas, Teofina A. Rapanut
Mathematics Faculty Publications
In this paper, we contribute to the study of colored symmetrical tilings by giving formulas for their associated color fixing groups. In the second part of the paper we provide an application of the results in describing symmetry groups of nanostructures.