Relevant bibliographies by topics / Regular polygons

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

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. 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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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 polygonal knots can be seen as a discrete version of the Lissajous knots.
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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 regular polygons to show that hexagonal tiling is the most efficient way to tessellate the plane in terms of the total perimeter per area coverage.</p>
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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 include regular polygons and triangles, especially isosceles: the variational estimate $R(\beta )$ is a rational function which approximates $Q(\beta )$ closely.
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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. 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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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 patterns and relationships between the areas of polygons and those of their associated midpoint polygons for triangles, quadrilaterals, pentagons, and other polygons. We shall also look at the pattern for regular polygons.
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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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Submitted by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-05-19T19:39:45Z No. of bitstreams: 1 arquivototal.pdf: 2901630 bytes, checksum: d49c78ad5c7d463bdc9e8f53c093d865 (MD5)<br>Approved for entry into archive by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-05-19T19:39:55Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 2901630 bytes, checksum: d49c78ad5c7d463bdc9e8f53c093d865 (MD5)<br>Made available in DSpace on 2015-05-19T19:39:55Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2901630 bytes, checksum: d49c78ad5c7d463bdc9e8f53c093d865 (MD5) Previous issue date: 2013-07-16<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>In this work we present some constructions of the regular pentagon, the main one is a construction of Euclid found in his book The Elements. We also present some applications of this construction.<br>Neste trabalho, apresentamos algumas construções do pentágono regular, sendo a principal delas uma construção de Euclides encontrada no seu livro Os Elementos. Apresentamos, também, algumas aplicações desta construção.
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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 evidenciarà uma relaÃÃo entre a geometria e a Ãlgebra, em especial, a relaÃÃo entre os vÃrtices de um polÃgono regular e as raÃzes de polinÃmios de uma variÃvel com coeficientes racionais. Este tratamento algÃbrico nos levarà naturalmente ao conceito de construtibilidade de nÃmeros e pontos no plano de um corpo, o que exigirà o uso de extensÃes algÃbricas de corpos, e os critÃrios para a construtibi- lidade destes nos levarà a um critÃrio de construtibilidade dos polÃgonos pretendidos.<br>This work discusses basic geometric constructions and constructions of regular polygons with ruler and compass made respecting the rules or elementary operations used by the ancient Greeks. Such constructs are initially treated in a purely geometric form and, in order to find a criterion that can determine the possibility of construction of regular polygons, will be discussed by an algebraic bias. This algebraic treatment will show a relationship between geometry and algebra, in particular, the relationship between the vertices of a regular polygon and the roots of polynomials in a variable with rational coefficients. This algebraic treatment leads us naturally to the concept of constructibility of numbers and points in a field, which will require the use of algebraic field extensions, and the criteria for the constructibility of these leads to a criterion for constructibility of polygons.
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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 for irregular polygons. In this part we try to expose an example, created during our studies, for a pairing that generates a tiling of the hyperbolic plane by an irregular polygon. Also use the techniques developed by Mercio Botelho Faria, Catarina Mendes de Jesus and Panteleón D. R. Sanchez in [14] to obtain matching of edges of regular polygons through surgeries in surfaces associated with trivalent graphs.<br>Esta dissertação tem como objetivo o estudo de dois temas ligados a topologia e a geometria moderna. O primeiro destes temas é dedicado ao estudo de empacotamento e coberturas de discos do plano hiperbólico, no qual tratamos de estudar resultados devidos a Bavard (1996) [3]. Já o segundo tema que foi abordado se refere ao estudo de emparelhamento de arestas para polígonos irregulares. Nesta parte tratamos de expor um exemplo, criado durante nossos estudos, para um emparelhamento que gera um ladrilhamento do plano hiperbólico por um polígono irregular. Além disso utilizamos as técnicas desenvolvidas por Mercio Botelho Faria, Catarina Mendes de Jesus e Panteleón D. R. Sanchez em [14] para obtermos emparelhamentos de arestas de polígonos regulares por meio de cirurgias em superfícies associadas a grafos trivalentes.
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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 five solid platonics and we will demonstrate the Euler Characteristics, through induction. We will provide sample activities, which can be used in classrooms, in order to in uence positivetly the learning process of students. Therefore, such students will be able to better learn and understand the content, rather than just decorating the \formulas". We will also show an intuitive idea of calculating the area and volumes of solid platonics, which is something rarely demonstrated in textbooks. Further on, we will demonstrate how this topic is presented by the National Curriculum Parameters \Parâmetros Curriculares Nacionais (PCN)", and relate it to how it is developed and and taught since the first years of schools until the second year of High School, time in which this topic is more deeply studied. There are sample questions, which can be found in national examinations, such as Saresp (São Paulo's government exam) and ENEM (Federal government exam). Throughout this work you will be able to see imagens that were taken during a project envolving students from a second High School year, which was taken place a public school.
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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 potencialidades do Scratch para o estabelecimento de conexões matemáticas e que dificuldades surgem em atividades matemáticas que envolvam o Scratch. Trata-se de um estudo que visa compreender o envolvimento dos alunos na utilização de um recurso informático (o Scratch) para trabalhar a área da Matemática. Assim, no enquadramento teórico, procura-se clarificar o que se entende por aprender Matemática hoje e discutir o papel do Scratch no ensino e aprendizagem da Matemática. Em termos metodológicos, o estudo enquadra-se numa abordagem qualitativa de investigação e no paradigma interpretativo. Os dados foram recolhidos através da observação participante, recolha documental e entrevistas. Os resultados do estudo revelam que a grande maioria dos alunos esteve bastante interessada e envolvida em toda a atividade desenvolvida com o Scratch. Entre as razões para o seu interesse e envolvimento, estão a possibilidade de desenvolverem projetos em que tinham alguma autonomia e a oportunidade de partilharem questões/dúvidas bem como estratégias que utilizaram para as ultrapassar as suas dificuldades. Neste processo, consolidaram conhecimentos e compreenderam noções que ainda não tinham aprendido ou percebido até então. Além disso, vários alunos foram além daquilo que lhes foi solicitado como aconteceu, nomeadamente a propósito da “decoração” dos projetos e quando, na tentativa de programar a construção de alguns polígonos, descobriram como se desenham outros. Quanto às dificuldades experienciadas, houve algumas diferenças. Em geral, as maiores dificuldades foram a seleção dos comandos para a construção, no Scratch, dos dois primeiros polígonos regulares e a elaboração de registos escritos que descrevessem os raciocínios feitos. Estas dificuldades geraram, nalguns casos, uma desmotivação inicial que deixou de existir assim que os alunos começaram a compreender como se faziam as construções e os raciocínios que tinham de utilizar.<br>This report presents a study carried out under Stage III of the course of the school year 2013/2014, which is developed with a group of 4 th grade of the 1st cycle of elementary education. Its main objective is to understand the potentialities of Scratch for learning mathematics and the constraints that might arise during its use in the classroom. In particular, it aims to understand mathematical concepts and ideas that emerge in developing projects with Scratch, Scratch which potentialities for establishing mathematical connections and difficulties in mathematical activities involving Scratch. This is a study to understand the involvement of students in the use of a computer resource (Scratch) to work the area of mathematics. Thus, the theoretical framework, seek to clarify what is meant by learning mathematics today and discuss the role of Scratch in teaching and learning mathematics. In terms of methodology, the study was based on a qualitative research approach and on the interpretive paradigm. Data were collected through participant observation, interviews and document collection. The study results reveal that the vast majority of students was very interested and involved in any activity developed with Scratch. Among the reasons for their interest and involvement, are the capacity to develop projects where they had some autonomy and the opportunity to share questions/concerns and strategies they used to overcome their difficulties. In this process, the students consolidate knowledge and understand concepts that had not yet been able to realize until then. In addition, several students were beyond what they are asked for. This situation has arisen, in particular, concerning the "decoration" of projects and when, in an attempt to program the construction of some polygons, they figured out how to draw others. Regarding the difficulties experienced, there were some differences. In general, the main difficulties were the selection of commands for the construction in Scratch, of the first two regular polygons and the preparation of written records to describe their reasoning. These difficulties have generated, in some cases, an initial lack of motivation, which no longer exists as soon as the students began to understand how to do the constructions and the arguments they had to use.
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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 $mu(a)=begin{pmatrix} 0 &amp; -1 1 &amp; a+1 end{pmatrix}.$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 présentations de monoïde de $PSL_2(zb)$ par générateurs et relations.Par ailleurs, on introduit le morphisme d'indice associé `a l'abélianisé du rev^etement universel de $PSL_2(zb)$,le groupe $B_3$ des tresses `a trois brins. Interprété dans deux contextes différents,le morphisme d'indice est associé au nombre de "demi-tours".Ensuite, dans les quatrième et cinquième parties, on dénombre des sous-ensembles du noyau de $mu_{|{0,1}}$ etdu noyau de $mu$, bigradués par la longueur et l'indice. La suite des nombres de Catalan et d'autres diagonales du triangle de Catalan interviennentsimplement dans les résultats.Enfin, on présente l'origine géométrique de cette étude : on explicite le lien entre l'objectif premier de la thèse qui était l'étudedes polygones convexes entiers d'aire minimale et notre intéret pour le monoïde engendré par ces matrices particulières de $PSL_2(zb)$<br>In this thesis, we study a morphism of mono"id $mu$ between the free mono"id on the alphabet of integers $nb$and the modular group $PSL_2(zb)$ considered as a mono"id, defined for all integer $a$by $mu(a)=begin{pmatrix} 0 &amp; -1 1 &amp; a+1 end{pmatrix}.$ The Catalan Numbers arised naturally in the study ofsubsets of the kernel of the morphism $mu$.Firstly, we introduce two rewriting systems, one on the finite alphabet ${0,1}$, and the other on the infinite alphabet of integers $nb$. We proove that bothof these rewriting systems defines a mono"id presentation of $PSL_2(zb)$ by generators and relations.On another note, we introduce the morphism of loop associated to the abelianised of the universal covering group of $PSL_2(zb)$, the group $B_3$ ofbraid group on $3$ strands. In two different contexts, the morphism of loop is associated to the number of "half-turns".Then, in the fourth and the fifth parts, we numerate subsets of the kernel of $mu_{|{0,1}}$ and of the kernel of $mu$,bi-graduated by the morphism of lengthand the morphism of loop. The sequences of Catalan numbers and other diagonals of the Catalan triangle come into the results.Lastly, we present the geometrical origin of this research : we detail the connection between our first aim,which was the study of convex integer polygones ofminimal area, and our interest for the mono"id generated by these particular matrices of $PSL_2(zb)$
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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 relation aux objets dans la recherche. De ce point de vue, l'étude des travaux de Johannes Kepler à la recherche d'une harmonie du monde est particulièrement instructive. Nous proposons également, pour l'analyse des savoirs émergents en situation didactique, une utilisation d'outils liés à la sémiotique qui permet de mettre en évidence la dynamique de l'évolution des objets mathématiques. Nous pouvons finalement conclure quant à la possibilité de construire et mettre en œuvre des ≪ Situations Didactiques de Recherche de Problème ≫ assurant l'engagement du sujet dans la recherche, l'émergence et le développement d'objets mathématiques, la genèse de savoirs. L'étude nous conforte dans la nécessité d'une approche pragmatique des situations et la pertinence d'un regard différent sur les savoirs à l'école<br>The study of the emergence of knowledges in teaching situations not finalized by a prefabricated and pre-thought knowledge requires an upheaval of point of view, epistemological as well as didactic. For the study of learning situations in which the problem is the essence, we develop a new historical approach and we rethink the tools for didactic analyzes. We propose, then, for a particular problem, exploration of Archimedean tilings of the plane, a historical inquiry centered on the activity of the scientist in the process of research and on the influence of the relationship with objects. From this perspective, the study of Johannes Kepler’s work in search of a world harmony is particularly instructive. We also propose, for the analysis of the emerging knowledge in teaching situations, to use tools related to semiotics, which allows to highlight the dynamic of evolution of mathematical objects. We can finally conclude on the opportunity to build and implement “Didactic Situations of Problem Solving”, which ensure the commitment of the subject in the research, the emergence and development of mathematical objects, the genesis of knowledges. The study reinforces the necessity of a pragmatic approach of situations and the relevance of a different look at the knowledge at school
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Books on the topic "Regular polygons"

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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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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 circle and the polygon within which circle was circumscribed. Since the real area of the circle is between the areas of the inscribed and circumscribed polygons, the polygon areas gave the upper and lower limits to the area of the circle. Archimedes knew he had not found the exact value of π, but only an approximation within these limits. In this way, Archimedes showed that π is between 3 1/7 (223/71) and 3 10/71 (22/7). This research demonstrates that the value of π is 3.15 and can be represented by a fraction of integers, a/b, being therefore a Rational Number. It also demonstrates by means of an exercise that π = 3.15 is exact in 100% in the mathematical question.
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Regular Polygon Tessellations Activity Book. Tessellations, 2010.

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Book chapters on the topic "Regular polygons"

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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 examples are reported.
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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 that k can be O(n2) when the offset distance is greater than or equal to the local radius of curvature of the polygon, a regular occurrence in the creation of contour-parallel offset curves for NC pocket machining. Our O(n log n) recursive algorithm, derived from Voronoi diagram algorithms, computes the velocities of polygon vertices as a function of overall offset rate. By construction, our algorithm prunes a large proportion of locally invalid loops from the raw offset curve, eliminating all self-intersections in raw offsets of convex polygons and the “near-circular”, k proportional to O(n2) worst-case scenarios in non-convex polygons.
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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 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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