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Relevant bibliographies by topics / Regular polygons

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Academic literature on the topic 'Regular polygons'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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Journal articles on the topic "Regular polygons"

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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 (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. I

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Wang, Chao, та Zhongzi Wang. "The limit shapes of midpoint polygons in ℝ3". Journal of Knot Theory and Its Ramifications 28, № 10 (2019): 1950062. http://dx.doi.org/10.1142/s0218216519500627.

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For a polygon in the [Formula: see text]-dimensional Euclidean space, we give two kinds of normalizations of its [Formula: see text]th midpoint polygon by a homothetic transformation and an affine transformation, respectively. As [Formula: see text] goes to infinity, the normalizations will approach “regular” polygons inscribed in an ellipse and a generalized Lissajous curve, respectively, where the curves may be degenerate. The most interesting case is when [Formula: see text], where polygons with all its [Formula: see text]th midpoint polygons knotted are discovered and discussed. Such polyg

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Kaiser, M. J. "Regular Steiner polygons." Applied Mathematics Letters 11, no. 6 (1998): 43–47. http://dx.doi.org/10.1016/s0893-9659(98)00100-1.

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Donkoh, Elvis K., and Alex A. Opoku. "Optimal Geometric Disks Covering using Tessellable Regular Polygons." Journal of Mathematics Research 8, no. 2 (2016): 25. http://dx.doi.org/10.5539/jmr.v8n2p25.

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<p>Geometric Disks Covering (GDC) is one of the most typical and well studied problems in computational geometry. Geometric disks are well known 2-D objects which have surface area with circular boundaries but differ from polygons whose surfaces area are bounded by straight line segments. Unlike polygons covering with disks is a rigorous task because of the circular boundaries that do not tessellate. In this paper, we investigate an area approximate polygon to disks that facilitate tiling as a guide to disks covering with least overlap difference. Our study uses geometry of tessellable r

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MILLETT, KENNETH C. "KNOTTING OF REGULAR POLYGONS IN 3-SPACE." Journal of Knot Theory and Its Ramifications 03, no. 03 (1994): 263–78. http://dx.doi.org/10.1142/s0218216594000204.

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The probability that a linear embedding of a regular polygon in R3 is knotted should increase as a function of the number of sides. This assertion is investigated by means of an exploration of the compact variety of based oriented linear maps of regular polygons into R3. Asymptotically, an estimation of the probability of knotting is made by means of the HOMFLY polynomial.

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Keady, Grant. "Steady slip flow of Newtonian fluids through tangential polygonal microchannels." IMA Journal of Applied Mathematics 86, no. 3 (2021): 547–64. http://dx.doi.org/10.1093/imamat/hxab008.

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Abstract The concern in this paper is the problem of finding—or, at least, approximating—functions, defined within and on the boundary of a tangential polygon, functions whose Laplacian is $-1$ and which satisfy a homogeneous Robin boundary condition on the boundary. The parameter in the Robin condition is denoted by $\beta $. The integral of the solution over the interior, denoted by $Q$, is, in the context of flows in a microchannel, the volume flow rate. A variational estimate of the dependence of $Q$ on $\beta $ and the polygon’s geometry is studied. Classes of tangential polygons treated

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Friedenberg, Jay. "The Perceived Beauty of Regular Polygon Tessellations." Symmetry 11, no. 8 (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

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McLean, K. Robin. "Loops of Regular Polygons." American Mathematical Monthly 107, no. 6 (2000): 500–510. http://dx.doi.org/10.1080/00029890.2000.12005229.

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McLean, K. Robin. "Loops of Regular Polygons." American Mathematical Monthly 107, no. 6 (2000): 500. http://dx.doi.org/10.2307/2589345.

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Gau, Y. David, and Lindsay A. Tartre. "The Sidesplitting Story of the Midpoint Polygon." Mathematics Teacher 87, no. 4 (1994): 249–56. http://dx.doi.org/10.5951/mt.87.4.0249.

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Understanding what area means and learning ways to calculate the area of various figures are important objectives in geometry. Students as adults will use concepts related to finding areas of polygons in many contexts, such as finding the area of their backyard or knowing how much wallpaper is needed to cover a wall in their dining room. One context for exploring area relationships is comparing the area of a polygon to the area of its associated midpoint polygon, formed by joining the midpoints of consecutive sides of the original polygon. This article describes activities that examine the pat

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Dissertations / Theses on the topic "Regular polygons"

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Lenngren, Nils. "k-uniform tilings by regular polygons." Thesis, Uppsala universitet, Algebra, geometri och logik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159395.

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Carroll, Kathleen Mary. "Determining the number of loops of regular polygons /." Norton, Mass. : Wheaton College, 2010. http://hdl.handle.net/10090/15512.

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Silva, Alex Cristophe Cruz da. "A construção do pentágono regular segundo Euclides." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7483.

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Lopes, Aislan Sirino. "CritÃrio para a construtibilidade de polÃgonos regulares por rÃgua e compasso e nÃmeros construtÃveis." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12590.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Este trabalho aborda construÃÃes geomÃtricas elementares e de polÃgonos regulares realizadas com rÃgua nÃo graduada e compasso respeitando as regras ou operaÃÃes elementares usadas na Antiguidade pelos gregos. Tais construÃÃes serÃo inicialmente tratadas de uma forma puramente geomÃtrica e, a fim de encontrar um critÃrio que possa determinar a possibilidade de construÃÃo de polÃgonos regulares, passarÃo a ser discutidas por um viÃs algÃbrico. Este tratamento algÃbrico evidenciarÃ uma relaÃÃo entre a geometria e a Ãlgebra, em especi

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Batista, Frederico Ventura. "Ladrilhamentos irregulares, discos extremos e grafos de balão." Universidade Federal de Viçosa, 2012. http://locus.ufv.br/handle/123456789/4915.

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Made available in DSpace on 2015-03-26T13:45:34Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1893968 bytes, checksum: ce37a1814e775a74aa222b17583fdc19 (MD5) Previous issue date: 2012-02-28<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>This dissertation aims to study two topics related to modern topology and geometry. The first of these themes is dedicated to the study of packaging and record covering spheres in the hyperbolic plane, in which we treat the study results due to Bavard (1996) [3]. The second issue that was addressed refers to the study of edges pairing fo

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DeSouza, Chelsea E. "The Greek Method of Exhaustion: Leading the Way to Modern Integration." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658.

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Nogueira, Simone Paes Gonçalves. "Poliedros de Platão como estratégia no ensino da geometria espacial." reponame:Repositório Institucional da UFABC, 2014.

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Orientador: Prof. Dr. André Ricardo Oliveira da Fonseca<br>Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2014.<br>Our work aims to make a brief study on polyhedrons, focusing specially on solid platonics. First, we will present the historical moment in which this topic was discussed, as well as mention the mathematicians who contributed to the first studies about it. Then, we will explain what are regular polygons, dihedral angle and regular polyhedron. We will also discuss the reasons why there are only

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Correia, Tânia Filipa Martins. "Scratch na aprendizagem da matemática." Master's thesis, Escola Superior de Educação, Instituto Politécnico de Setúbal, 2013. http://hdl.handle.net/10400.26/6568.

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Mestrado em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico<br>Este trabalho apresenta um estudo, realizado no âmbito da Unidade Curricular Estágio III do ano letivo 2013/2014, que se desenvolveu com alunos do 4º ano de escolaridade de uma turma do 1º Ciclo do Ensino Básico. O seu principal objetivo é compreender as potencialidades do Scratch para a aprendizagem da Matemática e os constrangimentos que podem surgir durante a sua utilização na aula. Em particular, pretende-se perceber que ideias e conceitos matemáticos emergem no desenvolvimento de projetos com o Scratch, quais as pot

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Guichard, Christelle. "Les nombres de Catalan et le groupe modulaire PSL2(Z)." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAM057/document.

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Dans ce mémoire de thèse, on étudie le morphisme de monoïde $mu$du monoïde libre sur l'alphabet des entiers $nb$,`a valeurs dans le groupe modulaire $PSL_2(zb)$,considéré comme monoïde, défini pour tout entier $a$ par $mu(a)=begin{pmatrix} 0 & -1 1 & a+1 end{pmatrix}.$Les nombres de Catalan apparaissent naturellement dans l'étudede sous-ensembles du noyau de $mu$.Dans un premier temps, on met en évidence deux systèmes de réécriture, l'un sur l'alphabet fini ${0,1}$, l'autresur l'alphabet infini des entiers $nb$ et on montreque ces deux systèmes de réécriture définissent des présentatio

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Front, Mathias. "Émergence et évolution des objets mathématiques en Situation Didactique de Recherche de Problème : le cas des pavages archimédiens du plan." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10250/document.

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Étudier l'émergence de savoirs lors de situations didactiques non finalisées par un savoir préfabriqué et pré-pensé nécessite un bouleversement des points de vue, aussi bien épistémologique que didactique. C'est pourquoi, pour l'étude de situations didactiques pour lesquelles le problème est l'essence, nous développons une nouvelle approche historique et repensons des outils pour les analyses didactiques. Nous proposons alors, pour un problème particulier, l'exploration des pavages archimédiens du plan, une enquête historique centrée sur l'activité du savant cherchant et sur l'influence de la

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Books on the topic "Regular polygons"

1

Lexicographical manipulations for correctly computing regular tetrahedralizations with incremental topological flipping. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1999.

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2

Chen, Fen. Regular Polygons: Applied New Theory of Trisection to Construct a Regular Heptagon for Centuries in the History of Mathematics. International School Math & Sciences Institut, 2001.

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3

Silva, Sidney. A ousadia do π ser racional. Brazil Publishing, 2020. http://dx.doi.org/10.31012/978-65-5861-280-3.

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Pi (π) is used to represent the most known mathematical constant. By definition, π is the ratio of the circumference of a circle to its diameter. In other words, π is equal to the circumference divided by the diameter (π = c / d). Conversely, the circumference is equal to π times the diameter (c = π . d). No matter how big or small a circle is, pi will always be the same number. The first calculation of π was made by Archimedes of Syracuse (287-212 BC) who approached the area of a circle using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the c

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Regular Polygon Tessellations Activity Book. Tessellations, 2010.

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Book chapters on the topic "Regular polygons"

1

Stewart, Ian. "Regular polygons." In Galois Theory. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-0839-0_17.

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Delahaye, Jean-Paul. "Regular Polygons, Stars etc." In Geometric and Artistic Graphics. Macmillan Education UK, 1986. http://dx.doi.org/10.1007/978-1-349-08770-9_1.

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Strick, Heinz Klaus. "Partitions of Regular Polygons." In Mathematics is Beautiful. Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-62689-4_8.

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Strick, Heinz Klaus. "Regular Polygons and Stars." In Mathematics is Beautiful. Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-62689-4_1.

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Leimbach, Judy, Kathy Leimbach, and Mary Lou Johnson. "Regular Polygons and Angles." In Math Extension Units. Routledge, 2021. http://dx.doi.org/10.4324/9781003236481-23.

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Bewersdorff, Jörg. "The construction of regular polygons." In Galois Theory for Beginners. American Mathematical Society, 2006. http://dx.doi.org/10.1090/stml/035/07.

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Artmann, Benno. "Euclid Book IV: Regular Polygons." In Euclid—The Creation of Mathematics. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1412-0_11.

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Meskens, Ad, and Paul Tytgat. "The Cinderella of regular polygons." In Compact Textbooks in Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-42863-5_8.

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Kovács, Zoltán. "Discovering Geometry Theorems in Regular Polygons." In Artificial Intelligence and Symbolic Computation. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99957-9_10.

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Štola, Jan. "3D Visibility Representations by Regular Polygons." In Graph Drawing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11805-0_31.

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Conference papers on the topic "Regular polygons"

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Figliolini, Giorgio, Pierluigi Rea, and Salvatore Grande. "Kinematic Synthesis of Rotary Machines Generated by Regular Curve-Polygons." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71192.

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This paper deals with the kinematic synthesis of volumetric rotary machines, which are generated by the planetary motion of regular curve-polygons. In particular, the synthesis of both outer and inner conjugate profiles has been formulated as envelope of the polycentric profiles of a generating regular curve-polygon with any number of lobes, different radii of the circumcircle and rounded corners. A regular curve-polygon with cusp corners can be obtained as a particular case, like the Reuleaux triangle. Finally, the proposed formulation has been implemented in a Matlab code and several example

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Medeiros e Sa, Asla, Luiz Henrique de Figueiredo, and Jose Ezequiel Soto Sanchez. "Synthesizing Periodic Tilings of Regular Polygons." In 2018 31st SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI). IEEE, 2018. http://dx.doi.org/10.1109/sibgrapi.2018.00009.

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Chen, Li, Jianping Zhang, and Donald H. Cooley. "Regular polygons and their application to digital curves." In SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, edited by Robert A. Melter, Angela Y. Wu, and Longin J. Latecki. SPIE, 1996. http://dx.doi.org/10.1117/12.251786.

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Ambuj, Anindya, Reeta Vyas, and Surendra Singh. "Diffraction of Laguerre-Gauss vortex beams by regular polygons." In Frontiers in Optics. OSA, 2014. http://dx.doi.org/10.1364/fio.2014.jtu3a.10.

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Ida, Tetsuo, Fadoua Ghourabi, and Kazuko Takahashi. "Knot Fold of Regular Polygons: Computer-Assisted Construction and Verification." In 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2013. http://dx.doi.org/10.1109/synasc.2013.9.

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Guttmann, A. J. "Planar polygons; Regular, convex, almost convex, staircase and row convex." In Computer-aided statistical physics. AIP, 1992. http://dx.doi.org/10.1063/1.41939.

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Burton, Greg. "A Hybrid Approach to Polygon Offsetting Using Winding Numbers and Partial Computation of the Voronoi Diagram." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34303.

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In this paper we present a new, efficient algorithm for computing the “raw offset” curves of 2D polygons with holes. Prior approaches focus on (a) complete computation of the Voronoi Diagram, or (b) pair-wise techniques for generating a raw offset followed by removal of “invalid loops” using a sweepline algorithm. Both have drawbacks in practice. Robust implementation of Voronoi Diagram algorithms has proven complex. Sweeplines take O((n + k)log n) time and O(n + k) memory, where n is the number of vertices and k is the number of self-intersections of the raw offset curve. It has been shown th

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Lizhi Xie, Peng Li, Mingquan Zhou, and Xuesong Wang. "An clipping general polygons in regular girds algorithm base on successive encoding." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5619427.

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Feng, Yang, Qiong Wu, Keisuke Okamoto, et al. "A basic study on regular polygons recognition of central and peripheral vision field for virtual reality." In 2017 IEEE International Conference on Mechatronics and Automation (ICMA). IEEE, 2017. http://dx.doi.org/10.1109/icma.2017.8016080.

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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 linearizat

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