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Relevant bibliographies by topics / Cyclic groups and regular polygons

Academic literature on the topic 'Cyclic groups and regular polygons'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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Journal articles
Dissertations / Theses
Conference papers

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Journal articles on the topic "Cyclic groups and regular polygons"

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Rehman, Shafiq Ur, Ghulam Farid, Tayaba Tariq, and Ebenezer Bonyah. "Equal-Square Graphs Associated with Finite Groups." Journal of Mathematics 2022 (February 24, 2022): 1–6. http://dx.doi.org/10.1155/2022/9244325.

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The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x 2 = y 2 . We call this graph an equal-square graph of the finite group G , symbolized by E S G . Some interesting properties of E S G are studied. Moreover, examples of equal-square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units U n , and the finite abelian groups are constructed.

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Mullen, Gary L., and Harald Niederreiter. "The structure of a group of permutation polynomials." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (April 1985): 164–70. http://dx.doi.org/10.1017/s1446788700023016.

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AbstractLet Gq be the group of permutations of the finite field Fq of odd order q that can be represented by polynomials of the form ax(q+1)/2 + bx with a, b ∈ Fq. It is shown that Gq is isomorphic to the regular wreath product of two cyclic groups. The structure of Gq can also be described in terms of cyclic, dicyclic, and dihedral groups. It also turns out that Gq is isomorphic to the dymmetry group of a regular complex polygon.

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3

Nurfarah Zulkifli and Nor Muhainiah Mohd Ali. "RELATIVE COPRIME PROBABILITY FOR CYCLIC SUBGROUPS OF SOME DIHEDRAL GROUPS." Open Journal of Science and Technology 3, no. 4 (December 29, 2020): 314–21. http://dx.doi.org/10.31580/ojst.v3i4.1679.

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A dihedral group is a group of symmetries of a regular -sided polygon, in other words, a structured operation that will make n-gon to go back to itself through a solid motion. Many researchers have studied various fields of group theory using dihedral groups and one of them is the study of the coprime probability of a group and it is defined as the probability of a random pair of elements in a group G such that the greatest common divisor of the order of x and y, where x and y are in G, is equal to one. The coprime probability of G is then extended to the relative coprime probability G and it is defined as the probability that two randomly selected elements h from H and g from G where H is a subgroup of a group G such that the greatest common divisor of the order of h and order of g, is equal to one. In this research, the concentration is on the generalization of the relative coprime probability for cyclic subgroups of some dihedral groups.

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Donkoh, E. K., S. K. Amponsah, and A. A. Opoku. "Overlap Dimensions in Cyclic Tessellable Regular Polygons." Research Journal of Mathematics and Statistics 7, no. 2 (May 25, 2015): 11–16. http://dx.doi.org/10.19026/rjms.7.5274.

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BRUCKSTEIN, ALFRED M., GUILLERMO SAPIRO, and DORON SHAKED. "EVOLUTIONS OF PLANAR POLYGONS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 06 (December 1995): 991–1014. http://dx.doi.org/10.1142/s0218001495000407.

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Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affine-invariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygo nal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. In the second part, two possible polygonal analogues of the well-known Euclidean curve shortening flow are presented. The models follow from geometric considerations. Experimental results show that an arbitrary initial polygon converges to either regular or irregular polygonal approximations of circles when evolving according to the proposed Euclidean flows.

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Chinyere, Ihechukwu, and Gerald Williams. "Generalized polygons and star graphs of cyclic presentations of groups." Journal of Combinatorial Theory, Series A 190 (August 2022): 105638. http://dx.doi.org/10.1016/j.jcta.2022.105638.

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Friedenberg, Jay. "The Perceived Beauty of Regular Polygon Tessellations." Symmetry 11, no. 8 (August 2, 2019): 984. http://dx.doi.org/10.3390/sym11080984.

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Beauty judgments for regular polygon tessellations were examined in two experiments. In experiment 1 we tested the three regular and eight semi-regular tilings characterized by a single vertex. In experiment 2 we tested the 20 demi-regular tilings containing two vertices. Observers viewed the tessellations at different random orientations inside a circular aperture and rated them using a numeric 1–7 scale. The data from the first experiment show a peak in preference for tiles with two types of polygons and for five polygons around a vertex. Triangles were liked more than other geometric shapes. The results from the second experiment demonstrate a preference for tessellations with a greater number of different kinds of polygons in the overall pattern and for tiles with the greatest difference in the number of polygons between the two vertices. Ratings were higher for tiles with circular arrangements of elements and lower for those with linear arrangements. Symmetry group p6m was liked the most and groups cmm and pmm were liked the least. Taken as a whole the results suggest a preference for complexity and variety in terms of both vertex qualities and symmetric transformations. Observers were sensitive to both the underlying mathematical properties of the patterns as well as their emergent organization.

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Conder, Marston D. E., and Thomas W. Tucker. "Regular Cayley maps for cyclic groups." Transactions of the American Mathematical Society 366, no. 7 (March 3, 2014): 3585–609. http://dx.doi.org/10.1090/s0002-9947-2014-05933-3.

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9

Williams, Gordon. "Petrie Schemes." Canadian Journal of Mathematics 57, no. 4 (August 1, 2005): 844–70. http://dx.doi.org/10.4153/cjm-2005-033-6.

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AbstractPetrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Gr¨unbaum–Dress polyhedra, possess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes.

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Riedl, Jeffrey M. "Automorphisms of Regular Wreath Product -Groups." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–12. http://dx.doi.org/10.1155/2009/245617.

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We present a useful new characterization of the automorphisms of the regular wreath product group of a finite cyclic -group by a finite cyclic -group, for any prime , and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut(), where is the regular wreath product of a finite cyclic -group by an arbitrary finite -group.

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Dissertations / Theses on the topic "Cyclic groups and regular polygons"

1

Emmett, Lynn. "Regular orbits of cyclic subgroups of the simple classical groups." Thesis, University of East Anglia, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426917.

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Tolmie, Julie, and julie tolmie@techbc ca. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." The Australian National University. School of Mathematical Sciences, 2000. http://thesis.anu.edu.au./public/adt-ANU20020313.101505.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. ¶ The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. ¶ The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.

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Tolmie, Julie. "Visualisation, navigation and mathematical perception: a visual notation for rational numbers mod1." Phd thesis, 2000. http://hdl.handle.net/1885/6969.

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There are three main results in this dissertation. The first result is the construction of an abstract visual space for rational numbers mod1, based on the visual primitives, colour, and rational radial direction. Mathematics is performed in this visual notation by defining increasingly refined visual objects from these primitives. In particular, the existence of the Farey tree enumeration of rational numbers mod1 is identified in the texture of a two-dimensional animation. The second result is a new enumeration of the rational numbers mod1, obtained, and expressed, in abstract visual space, as the visual object coset waves of coset fans on the torus. Its geometry is shown to encode a countably infinite tree structure, whose branches are cosets, nZ+m, where n, m (and k) are integers. These cosets are in geometrical 1-1 correspondence with sequences kn+m, (of denominators) of rational numbers, and with visual subobjects of the torus called coset fans. The third result is an enumeration in time of the visual hierarchy of the discrete buds of the Mandelbrot boundary by coset waves of coset fans. It is constructed by embedding the circular Farey tree geometrically into the empty internal region of the Mandelbrot set. In particular, coset fans attached to points of the (internal) binary tree index countably infinite sequences of buds on the (external) Mandelbrot boundary.

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Conference papers on the topic "Cyclic groups and regular polygons"

1

Zhou, Junyi, and Jing Shi. "Effect of Facility Geometry on RFID Localization Accuracy." In ASME 2009 International Manufacturing Science and Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/msec2009-84323.

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Radio frequency identification (RFID) is a promising technology for localization in various industrial applications. In RFID localization, accuracy is the top performance concern, and it is affected by multiple factors. In this paper, we investigate how the facility geometry impacts the expected localization accuracy in the entire region where the target is uniformly distributed. Three groups of geometries, namely, rectangles with various length-to-width ratios, circle, and regular polygons with 3–10 edges, are chosen for this study. A hybrid multilateration approach, which combines linearization and nonlinear optimization, is used to estimate the target location. Since the layout of landmarks significantly affects localization performance, we evaluate the expected accuracy in a facility obtained under the optimal landmark layout for the facility. The optimal landmark layout for each type of facility geometry is obtained, and then the effect of geometry is studied by comparing the expected accuracies of these layouts. It is discovered that (1) the optimal layouts follow several simple empirical deployment principles, (2) for all geometries, the expected accuracy improves and tends to reach the expected Cramer-Rao lower bound as more landmarks are used, and (3) if the same numbers of landmarks are used, the expected accuracies for circular and regular polygonal geometries are close. However, the expected accuracy for a rectangular geometry decreases as the length-to-width ratio increases.

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