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Dissertations / Theses on the topic 'Polygonal number'

Author: Grafiati
Published: 7 June 2025
Last updated: 2 August 2025

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1

Chipatala, Overtone. "Polygonal numbers." Kansas State University, 2016. http://hdl.handle.net/2097/32923.

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Master of Science<br>Department of Mathematics<br>Todd Cochrane<br>Polygonal numbers are nonnegative integers constructed and represented by geometrical arrangements of equally spaced points that form regular polygons. These numbers were originally studied by Pythagoras, with their long history dating from 570 B.C, and are often referred to by the Greek mathematicians. During the ancient period, polygonal numbers were described by units which were expressed by dots or pebbles arranged to form geometrical polygons. In his "Introductio Arithmetica", Nicomachus of Gerasa (c. 100 A.D), thoroughly
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2

Angeleska, Angela. "Combinatorial models for DNA rearrangements in ciliates." [Tampa, Fla] : University of South Florida, 2009. http://purl.fcla.edu/usf/dc/et/SFE0002998.

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3

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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4

Auger, Joseph Thomas. "Orbits of the Dissected Polygons of the Generalized Catalan Numbers." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302701692.

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5

Ogburn, Julia J. "Roots of Polynomials: Developing p-adic Numbers and Drawing Newton Polygons." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/scripps_theses/295.

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Newton polygons are constructions over the p-adic numbers used to find information about the roots of a polynomial or power series. In this the- sis, we will first investigate the construction of the field Qp on the p-adic numbers. Then, we will use theorems such as Eisenstein’s Irreducibility Criterion, Newton’s Method, Hensel’s Lemma, and Strassman’s Theorem to build and justify Newton polygons.
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6

Mott, Brittany Nicole. "Analysis of the Generalized Catalan Orbits." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750.

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7

Bureaux, Julien. "Méthodes probabilistes pour l'étude asymptotique des partitions entières et de la géométrie convexe discrète." Thesis, Paris 10, 2015. http://www.theses.fr/2015PA100160/document.

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Cette thèse se compose de plusieurs travaux portant sur l'énumération et le comportement asymptotique de structures combinatoires apparentées aux partitions d'entiers. Un premier travail s'intéresse aux partitions d'entiers bipartites, qui constituent une généralisation bidimensionnelle des partitions d'entiers. Des équivalents du nombre de partitions sont obtenus dans le régime critique où l'un des entiers est de l'ordre du carré de l'autre entier et au delà de ce régime critique. Ceci complète les résultats établis dans les années cinquante par Auluck, Nanda et Wright. Le deuxième travail tr
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8

Silva, Ronaldo Pires da. "Interseção de números geométricos via equação de Pell." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4793.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-10-27T14:48:51Z No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-27T14:53:07Z (GMT) No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<
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9

Santana, Erivaldo Ribeiro. "O problema da quadratura do círculo: uma abordagem histórica sob a perspectiva atual." Universidade Federal do Amazonas, 2015. http://tede.ufam.edu.br/handle/tede/4551.

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Submitted by Kamila Costa (kamilavasconceloscosta@gmail.com) on 2015-08-07T13:59:57Z No. of bitstreams: 1 Dissertacao - Erivaldo R. Santana.pdf: 3301648 bytes, checksum: f3e68eae0be26f8d67132dc1bd792d18 (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T14:09:31Z (GMT) No. of bitstreams: 1 Dissertacao - Erivaldo R. Santana.pdf: 3301648 bytes, checksum: f3e68eae0be26f8d67132dc1bd792d18 (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2015-08-07T14:11:00Z (GMT
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10

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 especi
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11

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 présentatio
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12

Motiejauskas, Danas. "Paprasto skylėto daugiakampio skaidymo algoritmai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100622_145747-56362.

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Baigiamajame magistro darbe nagrinėjama paprasto skylėto daugiakampio skaidymo į dalis, kurių viršūnių skaičius neviršyja nustatyto skaičiaus problema. Apibrėžiamas uždavinys ir jo svarba. Apžvelgiami egzistuojantys skaidymo algoritmai, padedantys išspręsti uždavinį, bei jų realizacijos. Pateikiamos trianguliacijos ir padalinimo į apytiksliai iškilius daugiakampius algoritmų modifikacijos, jų privalumai ir trūkumai. Įvertinamas šių modifikuotų algoritmų sudėtingumas. Eksperimentinėje dalyje pateikiami skaičiavimo eksperimentų rezultatai, jų analizė ir palyginimas su teoriniais algoritmų sudėti
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13

Chiconello, Luis Alexandre. "Números figurados e as sequências recursivas : uma atividade didática envolvendo números triangulares e quadrados." Universidade Federal de São Carlos, 2013. https://repositorio.ufscar.br/handle/ufscar/5931.

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Made available in DSpace on 2016-06-02T20:29:21Z (GMT). No. of bitstreams: 1 5050.pdf: 4225946 bytes, checksum: eef403ca886d7a47c3c8886fee5bc0f4 (MD5) Previous issue date: 2013-03-11<br>Financiadora de Estudos e Projetos<br>The shortage of activities regarding recursive defined sequences, allied to the importance of this theme to young students has been contested in at least twenty years of experience teaching Mathematics. The elaboration of a learning product, in a form of sheets of activities which gradually lead the student to the understanding of the concept of recursion, the pattern rec
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14

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,
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15

Alvarado, Alberto. "The role of interactive visualizations in the advancement of mathematics." Thesis, 2012. http://hdl.handle.net/2152/ETD-UT-2012-08-6163.

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This report explores the effect of interactive visualizations on the advancement of mathematics understanding. Not only do interactive visualizations aid mathematicians to expand the body of knowledge of mathematics but it also allows students an efficient way to process the information taught in schools. There are many concepts in mathematics that utilize interactive visualizations and examples of such concepts are illustrated within this report.<br>text
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16

Chen, Yu-Heng, and 陳佑恆. "Varying Numbers and Locations of Cutting Points for Polygon Turning." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/13509017345225901950.

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碩士<br>國立中興大學<br>機械工程學系所<br>98<br>The purpose of this research is to reduce the form error and increase the diversity of machinable shapes for polygon turning. Increasing the number of cutting points can reduce form error for prime-number sided polygons. For increasing shape diversity of polygon turning, a non-equilateral polygon with even-number sides can be produced by changing the distances from tool tips to the tool-disk center with speed ratio S=2. Combining milling and turning synchronously, the cutter and the workpiece simultaneously rotate with a constant speed ratio, polygon turning i
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17

Mehrabidavoodabadi, Saeed. "Geometric optimization problems on orthogonal polygons: hardness results and approximation algorithms." 2015. http://hdl.handle.net/1993/30984.

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In this thesis, we design and develop new approximation algorithms and complexity results for three guarding and partitioning problems on orthogonal polygons; namely, guarding orthogonal polygons using sliding cameras, partitioning orthogonal polygons so as to minimize the stabbing number and guarding orthogonal terrains using vertex guards. We first study a variant of the well-known art gallery problem in which sliding cameras are used to guard the polygon. We consider two versions of this problem: the Minimum- Cardinality Sliding Cameras (MCSC) problem in which we want to guard P with the m
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18

Tak-Man, Ma, and 馬德文. "Linear-Time Compression of Constant-Genus Polygon Meshes into Information-Theoretically Optimal Number of Bits." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/01181994682645779057.

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碩士<br>國立臺灣大學<br>資訊工程學研究所<br>91<br>Polygon mesh is an important primitive data structure for representing three-dimensional models. Its specification consists of topologic properties and geometric properties. The former describe the connectivity between nodes, edges and faces and the latter describe attributes such as node positions in 3D space, face colors, etc. Our interest is in the efficient encoding of topology, which is the bottleneck for 3D model compression. In the thesis, we provide a linear-time information-theoretically optimal compression algorithm for encoding (decoding) a constant
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19

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, a
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