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Academic literature on the topic 'Geometrical knowledge'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Journal articles on the topic "Geometrical knowledge":

Anderson, James A. D. W. "Representing geometrical knowledge." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 352, no. 1358 (August 29, 1997): 1129–39. http://dx.doi.org/10.1098/rstb.1997.0096.

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This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space–time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top–down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space–time. It can be used to match a prototype shape to an image, even in so called ‘accidental’ views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Dehaene, Stanislas, Véronique Izard, Pierre Pica, and Elizabeth Spelke. "Core Knowledge of Geometry in an Amazonian Indigene Group." Science 311, no. 5759 (January 20, 2006): 381–84. http://dx.doi.org/10.1126/science.1121739.

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Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Mundurukú, an isolated Amazonian indigene group. Mundurukú children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

Jayawardana, Chandana. "Geometrical Knowledge in Early Sri Lanka." History of Science in South Asia 10 (July 31, 2022): 44–67. http://dx.doi.org/10.18732/hssa69.

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This article addresses on history of mathematics (specially one of its specific branch, geometry) in Sri Lanka. Despite the large amount of research on the history of mathematics in India, China and the Middle East, that on Sri Lanka still remains limited. Sri Lanka had close relations with all these regions from ancient times and knowldge on mathematics should not be an alien subject there. This article tries to address the paucity of research on the history of mathematics in Sri Lanka while emphasizing the local character of that ancient knowldge.

Tièche, François, and Heinz Hügli. "From Topological Knowledge to Geometrical Map." IFAC Proceedings Volumes 31, no. 3 (March 1998): 81–86. http://dx.doi.org/10.1016/s1474-6670(17)44065-1.

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Werner, Markus, and Hans Stein. "Knowledge-based Engineering of Geometrical Data." ATZproduktion worldwide eMagazine 4, no. 1 (March 2011): 30–35. http://dx.doi.org/10.1365/s38312-011-0007-y.

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Tièche, François, and Heinz Hügli. "From topological knowledge to geometrical map." Control Engineering Practice 7, no. 6 (June 1999): 797–802. http://dx.doi.org/10.1016/s0967-0661(99)00026-x.

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Dal Magro, Tamires, and Manuel J. García-Perez. "On Euclidean diagrams and geometrical knowledge." THEORIA. An International Journal for Theory, History and Foundations of Science 34, no. 2 (September 25, 2019): 255. http://dx.doi.org/10.1387/theoria.20026.

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We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based practice strictly regimented, it is rooted in cognitive abilities that are universally shared.

Plotkin, T., and B. Plotkin. "Geometrical aspect of databases and knowledge bases." Algebra Universalis 46, no. 1 (June 2001): 131–61. http://dx.doi.org/10.1007/pl00000333.

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Salkov, Nikolay, and N. Kadikova. "Reforming of geometrical and graphic knowledge estimates." Геометрия и графика 1, no. 1 (June 14, 2013): 52–53. http://dx.doi.org/10.12737/475.

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Chen-Morris, Raz. "Geometry and the Making of Utopian Knowledge in Early Modern Europe." Nuncius 35, no. 2 (September 10, 2020): 387–412. http://dx.doi.org/10.1163/18253911-03502011.

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Abstract In his Della Pittura, Leon Battista Alberti initiated what I call a “utopian moment,” a philosophical and practical disposition fusing human ingenuity, geometry, and political harmony. This paper follows these notions as they evolved over the course of the sixteenth century and were embraced by the new science of Johannes Kepler and René Descartes, who reshaped these utopian dispositions with their new geometrical analyses of sight and light. In his Dioptrice, Kepler suggests a new science of refractions produced and manipulated artificially through lenses, their physical properties analyzed geometrically; in analyzing the rainbow, Descartes artificially reproduces it, initially through a glass flask filled with water, and then through a prism, thus giving a geometrical causal account of its colors. In both cases these analyses are entwined with subtle political metaphors, transforming the technical scientific issues into key features of a “utopian moment.”

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Dissertations / Theses on the topic "Geometrical knowledge":

Mak, Ming-wai. "The effects of geometer's sketchpad on mediating students' geometrical knowledge /." View the Table of Contents & Abstract, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35288279.

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Veronese, Paula Cristina de Faria [UNESP]. "O ensino de geometria no ciclo II do ensino fundamental: um estudo analítico." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/91174.

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Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-08-24Bitstream added on 2014-06-13T19:52:49Z : No. of bitstreams: 1 veronese_pcf_me_mar.pdf: 1927091 bytes, checksum: 69ba6b8cc05d6f0dd527c178c70ac5b3 (MD5)
Esta pesquisa tem como objeto de análise o Ensino da Geometria no Ciclo II do Ensino Fundamental e algumas implicações políticas pedagógicas que cercam este tema. Trabalho realizado inicialmente em duas salas de 5ª séries de uma Escola Pública Estadual, de um pequeno município às margens do Rio Tietê, na qual um grupo de 20 alunos e seus conhecimentos geométricos, foram o foco inicial desta investigação. Os alunos com idades entre dez e doze anos, pertencentes cada dez, respectivamente, a uma das duas classes de 5ª séries do período da manhã, tendo dois respectivos professores de Matemática, de metodologia e crenças pedagógicas diferentes: a construtivista e a tradicional, que nos levaram a realizar um total de 200 atividades - cada aluno foi avaliado com dez atividades que contemplam fazeres geométricos, pertinentes à Grade Curricular de Matemática. Estas foram analisadas de maneira qualitativa, e independente da crença metodológica do professor, na sua maioria os alunos apresentaram frágil e preocupante desempenho quanto aos conhecimentos geométricos. Tais resultados nos levam a ampliar os questionamentos, assim como os grupos pesquisados, que se completa com 20 professores de Matemática, que respondem a 140 questões sobre o objeto de estudo e seu questionamento principal, o pensamentos dos 2 Professores responsáveis pelas duas 5ª séries envolvidas na pesquisa, e depoimentos de 4 PCOPs – Professores Coordenadores de Matemática de 4 Oficinas Pedagógicas de Diretorias de Ensino do interior paulista. No universo de respostas analisadas, à luz de uma metodologia qualitativa, surgem apontamentos para a situação caótica do Ensino da Geometria. Quanto à categoria docente, as conseqüências de grande carência de conteúdos geométricos na sua Formação Acadêmica e outros que implicam diretamente na produção de conhecimentos matemáticos...
The object of this study is the teaching of Geometry in junior high school and the political and pedagogical implications connected to the theme. I conducted this research in two fifth grade classrooms from a public school of a small town located on the bank of the Tietê River. I initially surveyed a group of 20 students and their knowledge of Geometry. I chose 10 students from each class, ages ranging from 10 to 12 years old, who studied in the morning and had two different teachers whose approaches to the teaching of Geometry was diverse: one followed the traditional model whereas the other adopts Constructivism. With the students, we did 200 activities involving the knowledge of Geometry. Each student performed ten tasks about the syllabus of Geometry. Such tasks were qualitatively analyzed. Throughout the research, both my questionings and the groups enlarged and 20 Math teachers answered 140 questions about my object of study and its main questionings. Also answering the questions, the two teachers responsible for the classes as well as four teachers from different regional Boards of Education. When their answers were analyzed I noticed a lack of geometrical knowledge in their academic formation. Besides this scarce knowledge of the VAN HIELE theoretical bases of the subject they teach, other factors influence performance in class, such as the low salaries they get. These will have damaging effects on the students’ learning process and led me to conclude that we need more solid educational policies, capable of transforming this scenario. The study also shows a documental analysis of more than three decades of syllabuses elaborated by the State Board of Education of the state of São Paulo and ho the teaching of Geometry was carelessly handled.

Isik, Hakan. "Relationship of college student characteristics and inquiry-based geometrical optics instruction to knowledge of image formation with light-ray tracing." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1201718813.

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Veronese, Paula Cristina de Faria. "O ensino de geometria no ciclo II do ensino fundamental : um estudo analítico /." Marília : [s.n.], 2009. http://hdl.handle.net/11449/91174.

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Orientador: José Carlos Miguel
Banca: Nelson Antonio Pirola
Banca: Dagoberto Buim Arena
Resumo: Esta pesquisa tem como objeto de análise o Ensino da Geometria no Ciclo II do Ensino Fundamental e algumas implicações políticas pedagógicas que cercam este tema. Trabalho realizado inicialmente em duas salas de 5ª séries de uma Escola Pública Estadual, de um pequeno município às margens do Rio Tietê, na qual um grupo de 20 alunos e seus conhecimentos geométricos, foram o foco inicial desta investigação. Os alunos com idades entre dez e doze anos, pertencentes cada dez, respectivamente, a uma das duas classes de 5ª séries do período da manhã, tendo dois respectivos professores de Matemática, de metodologia e crenças pedagógicas diferentes: a construtivista e a tradicional, que nos levaram a realizar um total de 200 atividades - cada aluno foi avaliado com dez atividades que contemplam fazeres geométricos, pertinentes à Grade Curricular de Matemática. Estas foram analisadas de maneira qualitativa, e independente da crença metodológica do professor, na sua maioria os alunos apresentaram frágil e preocupante desempenho quanto aos conhecimentos geométricos. Tais resultados nos levam a ampliar os questionamentos, assim como os grupos pesquisados, que se completa com 20 professores de Matemática, que respondem a 140 questões sobre o objeto de estudo e seu questionamento principal, o pensamentos dos 2 Professores responsáveis pelas duas 5ª séries envolvidas na pesquisa, e depoimentos de 4 PCOPs - Professores Coordenadores de Matemática de 4 Oficinas Pedagógicas de Diretorias de Ensino do interior paulista. No universo de respostas analisadas, à luz de uma metodologia qualitativa, surgem apontamentos para a situação caótica do Ensino da Geometria. Quanto à categoria docente, as conseqüências de grande carência de conteúdos geométricos na sua Formação Acadêmica e outros que implicam diretamente na produção de conhecimentos matemáticos... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The object of this study is the teaching of Geometry in junior high school and the political and pedagogical implications connected to the theme. I conducted this research in two fifth grade classrooms from a public school of a small town located on the bank of the Tietê River. I initially surveyed a group of 20 students and their knowledge of Geometry. I chose 10 students from each class, ages ranging from 10 to 12 years old, who studied in the morning and had two different teachers whose approaches to the teaching of Geometry was diverse: one followed the traditional model whereas the other adopts Constructivism. With the students, we did 200 activities involving the knowledge of Geometry. Each student performed ten tasks about the syllabus of Geometry. Such tasks were qualitatively analyzed. Throughout the research, both my questionings and the groups enlarged and 20 Math teachers answered 140 questions about my object of study and its main questionings. Also answering the questions, the two teachers responsible for the classes as well as four teachers from different regional Boards of Education. When their answers were analyzed I noticed a lack of geometrical knowledge in their academic formation. Besides this scarce knowledge of the VAN HIELE theoretical bases of the subject they teach, other factors influence performance in class, such as the low salaries they get. These will have damaging effects on the students' learning process and led me to conclude that we need more solid educational policies, capable of transforming this scenario. The study also shows a documental analysis of more than three decades of syllabuses elaborated by the State Board of Education of the state of São Paulo and ho the teaching of Geometry was carelessly handled.
Mestre

Sönnerhed, Wang Wei. "Mathematics textbooks for teaching : An analysis of content knowledge and pedagogical content knowledge concerning algebra in Swedish upper secondary education." Licentiate thesis, Institutionen för pedagogik, kommunikation och lärande, Göteborgs universitet, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-16949.

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In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.

Zhang, Kefei. "Geometric model input and feature recognition knowledge base for EXCAP." Thesis, University of Manchester, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330310.

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Bridge, Steven Frank. "Aspects of the geometric representation of knowledge for computer aided design." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/46974.

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Abbas, Ayman. "A modelling approach to individualised computer aided learning for geometric design." Thesis, University of Strathclyde, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324096.

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Diligenti, Marcos Pereira. "A geometria da complexidade." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2006. http://hdl.handle.net/10183/8559.

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Esta tese consiste em um estudo sobre a concepção do conhecimento da Geometria nos cursos superiores de Arquitetura. Durante três semestres, desenvolvemos uma proposta de abordagem transdisciplinar no ensino da Geometria Descritiva, junto a seis turmas de estudantes da Pontifícia Universidade Católica do Rio Grande do Sul, que se constituiu no ensino dos conceitos geométricos, compreendidos em suas relações e interdependências com seus entornos histórico / culturais/ filosóficos/ epistemológicos. Aliados a esta postura, introduzimos os conceitos genéricos de solidariedade e criatividade, na forma de migrações conceituais pelos campos geométrico/arquitetônicos, como instrumento instigador do resgate na compreensão da humanidade do conhecimento científico. Discutimos, neste estudo, a receptividade dos estudantes em relação a estas abordagens e às dificuldades verificadas no desenvolvimento destas propostas. Para analisar a concepção de conhecimento advinda destas implementações, utilizamos como referencial teórico o Paradigma da Complexidade, na ótica de Edgar Morin. Finalizando este trabalho, aproximamos as nossas interpretações do conceito de utopia, na perspectiva de Ernst Bloch, na qual encontramos a reafirmação do movimento como componente central dos fenômenos estudados, com a evidência de sua inexorabilidade na compreensão do conhecimento, do ser humano e da vida.
This thesis is a study about the conception of knowledge on Geometry in the graduation programs of Architecture. For three semesters we have developed a proposal of a cross disciplinary approach in the teaching of Descriptive Geometry with six groups of architecture students from the Pontifical Catholic University of Rio Grande do Sul. The proposal involved the teaching of geometric concepts and their relationships and interdependencies with historical, cultural, philosophical and epistemological contours. Along with such approach, we have introduced generic concepts of solidarity and creativity in the form of conceptual migrations through geometric and architectural fields, as an instigating instrument to rescue the understanding of the humanitarian aspect of scientific knowledge. We discussed, in this study, the receptive attitude from the students in terms of these approaches and the difficulties faced in order to develop them. To analyze the concept of knowledge resulting from such implementations, we used as theoretical background the Paradigm of Complexity, in the view of Edgar Morin. We finally approximated our interpretations to the concept of utopia, in the perspective by Ernst Bloch, in which we found the reaffirmation of movement as the central component of the investigated phenomena, with the evidence of its inexorability in the understanding of knowledge, human beings and life.

Bento, Regina Thaise Ferreira. "Um estudo das geometrias prática e teórica presentes em The Pathewaie to Knowledge de Robert Recorde: possíveis diálogos." Pontifícia Universidade Católica de São Paulo, 2018. https://tede2.pucsp.br/handle/handle/21657.

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Made available in DSpace on 2018-11-28T09:08:47Z (GMT). No. of bitstreams: 1 Regina Thaise Ferreira Bento.pdf: 2460878 bytes, checksum: a76eef8a10c705202f8c54f9b7f22996 (MD5) Previous issue date: 2018-08-27
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In this work we present the English mathematician Robert Record (1512-1558) and his treatise on geometry titled The Pathewaie to Knowledge, written in modern English and whose first edition was printed in the year 1551. We analyze in this treatise the presence and possible dialogue established between the geometric knowledge from ancient traditions linked to practice and the theoretical geometry that is studied in the universities and is based on the geometric treatise written by Euclides. To do so, we analyze the context in which the work and its author were inserted, identify what mathematical knowledge is present in this treatise and how they relate to the mathematical practices and the scholarly knowledge of the time. In addition, we sought indications that would allow us to evidence the presence of other geometric. This analysis was made use of the articulation between three spheres: the historiographical, the contextual and the epistemological. This combination gave us a broader look at the possible motivations that would have led Recorde to write the treatise in question. We find that Record was a man cultivated and attentive to the demands of his people and his time. Sixteenth-century England was at a time of social, political, and religious transformation; there was a great demand for investments in the practical-oriented sciences such as artillery, horology, navigation, and land measurement. Thus, professionals such as land surveyors and navigators assumed a determining role for the development of England and needed greater mathematical knowledge to advance their practices. However, access to education was restricted to most of the population and the little available material was written in Latin. This demand for mathematical knowledge practiced in this period, such as arithmetic, algebra, and geometry, made professionals who mastered their craft begin to produce materials written in the vernacular. Recorde, with his privileged background, was the first to produce a collection of textbooks in English with basic mathematics aimed directly at the interests of these professionals. The Pathewaie to Knowledge was the first treatise on practical geometry written in English. At that time practical and theoretical geometry were independent. With the results of this work it is concluded that in fact Robert Record established a dialogue between practical and theoretical geometries, contributing to the dissemination of speculative mathematical knowledge and the validation of geometry used for centuries by mathematicians. This analysis indicates that the understanding of the process that involves the construction of mathematical knowledge can effectively aid in a more critical learning by mathematical educators
Neste trabalho, apresentamos o matemático inglês Robert Recorde (1512-1558) e seu tratado sobre geometria entitulado The Pathewaie to Knowledge, escrito em inglês moderno e cuja primeira edição foi impressa no ano de 1551. Analisamos neste tratado a presença e possível diálogo estabelecidos entre os conhecimentos geométricos provenientes de antigas tradições ligadas à prática e a geometria teórica que era estudada nas universidades e baseada no tratado geométrico escrito por Euclides. Para tanto, analisamos o contexto no qual a obra e seu autor estavam inseridos, identificamos quais os conhecimentos matemáticos estão presentes nesse tratado e como se relacionam com as práticas matemáticas e o saber erudito da época. Além disso, procuramos indícios que nos permitissem evidenciar a presença de outras tradições geométricas. Esta análise utilizou-se da articulação entre três esferas: a historiográfica, a contextual e a epistemológica. Essa junção permitiu-nos um olhar ampliado sobre as possíveis motivações que teriam levado Recorde a escrever o tratado em questão. Verificamos que Recorde era um homem culto e atento às demandas de seu povo e de seu tempo. A Inglaterra do século XVI estava em um momento de transformação social, política e religiosa, havia uma grande demanda por investimentos nas ciências voltadas às questões práticas, tais como a artilharia, horologia, navegação e medição de terras. Assim, profissionais tais como os agrimensores e navegadores assumiram um papel determinante para o desenvolvimento da Inglaterra e necessitavam de maiores conhecimentos matemáticos para avançarem em suas práticas. Contudo, o acesso ao ensino era restrito para a maioria da população e o pouco material disponível era escrito em latim. Essa demanda por conhecimentos voltados às matemáticas praticadas neste período, tais como aritmética, álgebra e geometria fez com que profissionais que dominavam seus ofícios começassem a produzir materiais escrevendo-os na língua vernacular. Recorde, com sua formação privilegiada, foi o primeiro a elaborar uma coleção de livros textos em inglês com matemática básica voltada diretamente aos interesses desses profissionais. The Pathewaie to Knowledge foi o primeiro tratado sobre geometria prática escrito em inglês. Nesse período a geometria prática e teórica eram independentes. Com os resultados desse trabalho conclui-se que de fato Robert Recorde estabeleceu um diálogo entre as geometrias prática e teórica, contribuindo com a disseminação dos conhecimentos matemáticos especulativos e a validação da geometria utilizada há séculos pelos praticantes das matemáticas. Essa análise indica que a compreensão do processo que envolve a construção de conhecimentos matemáticos pode auxiliar de forma efetiva em uma aprendizagem mais crítica pelos educadores matemáticos

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Books on the topic "Geometrical knowledge":

Santi, Raffaella. Ragione geometrica e legge in Thomas Hobbes. [Padua, Italy]: CEDAM, 2012.

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Renz, Ursula. Die Erklärbarkeit von Erfahrung: Realismus und Subjektivität in Spinozas Theorie des menschlichen Geistes. Frankfurt: Klostermann, 2010.

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Sal'kov, Nikolay. Descriptive geometry: Designing surfaces. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1196545.

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In the textbook, in addition to the geometric design of surfaces, the elements of analytical and parametric geometries are proposed that contribute to the design and bring the result to a higher level of knowledge, as well as a frame method for designing surfaces. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of the specialties "Architect" and " Designer of the architectural environment "(qualifications "bachelor", "specialist", "master"). It may be useful for students of other fields of study.

Hoyrup, Jens. Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique - Max PlanckResearch Library for the History and Development of Knowledge - Textbooks 2. Pro Business, 2017.

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Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

Mann, Peter. Differential Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0038.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

Spinoza, Benedictus de. The Ethics: Ethica Ordine Geometrico Demonstrata. IndyPublish.com, 2006.

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Huybrechts, D. Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.001.0001.

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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.

Nagarajan, Vijaya. Embodied Mathematics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780195170825.003.0007.

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This chapter introduces ethnomathematics and discusses the multiple relationships between the kōlam and mathematics. Some of these mathematical properties align with women’s implicit framing knowledge of the kōlam. These ritual patterns are relevant to four key mathematical aspects: symmetry, fractals, array grammars and picture languages, and infinity. This chapter presents the concept of embodied mathematics and argues that Chandralekha’s choreographies embody the three dimensional kōlam. The dot kōlams and the square kōlams are symmetrical. Using geometric algorithms, mathematicians have found that the kōlam is created by transforming and superimposing basic subunits into fractals. Picture languages use sets of basic units combined with formal rules to make larger and seemingly infinite patterns, which computer scientists use for programming computer languages. The kōlam’s connection to infinity serves as a vehicle for auspiciousness. This chapter also discusses how Chandralekha’s choreographies expand the two-dimensional kōlam into three dimensions.

The Pathway to Knowledge: Containing the first principles of Geometrie, as they may most aptly be applied unto practise, both for use of instruments Geometricall, and astronomicall and also for projection of plattes in every kinde, and therfore much necessary for all sortes of men. Mickleover, Derby, United Kingdom: TGR Renascent Books, 2009.

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Book chapters on the topic "Geometrical knowledge":

Zhang, Junping, Stan Z. Li, and Jue Wang. "Geometrical Probability Covering Algorithm." In Fuzzy Systems and Knowledge Discovery, 223–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11539506_29.

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Magnani, Lorenzo. "At the Origins of Geometrical Knowledge." In The Western Ontario Series in Philosophy of Science, 1–26. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-9622-5_1.

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Magnani, Lorenzo. "The Φαντασία in Ancient Geometrical Knowledge." In The Western Ontario Series in Philosophy of Science, 91–103. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-9622-5_4.

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Homan, Matthew. "Intuitive Knowledge: The Perfection of Reason." In Spinoza’s Epistemology through a Geometrical Lens, 181–226. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76739-6_7.

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Hoyles, Celia. "Modelling Geometrical Knowledge: The Case of the Student." In Intelligent Learning Environments: The Case of Geometry, 94–112. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-60927-5_7.

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Sebban, M., S. Rabaseda, and O. Boussaid. "Contribution of Related Geometrical Graphs in Pattern Recognition." In Studies in Classification, Data Analysis, and Knowledge Organization, 167–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-61159-9_15.

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Koh, Sungshik, and Phil Jung Kim. "Uncertainty Analysis Using Geometrical Property Between 2D-to-3D Under Affine Projection." In Fuzzy Systems and Knowledge Discovery, 898–907. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11881599_112.

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Rasson, Jean-Paul, Didier Jacquemin, and Vincent Bertholet. "A new geometrical hypothesis for clustering and discriminant analysis." In Studies in Classification, Data Analysis, and Knowledge Organization, 257–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-72253-0_36.

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Janning, Ruth, Tomáš Horváth, Andre Busche, and Lars Schmidt-Thieme. "GamRec: A Clustering Method Using Geometrical Background Knowledge for GPR Data Preprocessing." In IFIP Advances in Information and Communication Technology, 347–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33409-2_36.

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Favi, Claudio, Marco Mandolini, Federico Campi, Paolo Cicconi, Roberto Raffaeli, and Michele Germani. "Design for Manufacturing and Assembly: A Method for Rules Classification." In Lecture Notes in Mechanical Engineering, 354–59. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70566-4_56.

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AbstractThe paper provides a method to acquire, process, and represent DfMA rules to help designers and engineers in the development of mechanical products compliant with manufacturing and assembly technology. This research work wants to define a general method able to link DfMA design guidelines (knowledge engineering) with geometrical product features that are available by the investigation of the 3D model. Numerical parameters of design features are related to design guidelines for the identification of manufacturing and assembly issues within the analysis of the 3D model.

Conference papers on the topic "Geometrical knowledge":

Yaghouti Jafarabad, Majid, Vahid Kiani, Taha Hamedani, and Ahad Harati. "Depth image compression using geometrical wavelets." In 2014 6th Conference on Information and Knowledge Technology (IKT). IEEE, 2014. http://dx.doi.org/10.1109/ikt.2014.7030344.

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Malhotra, Reetu, Isheta Bansal, Muskan, and Mamtha Sandhu. "The smart anti COVID cradle with geometrical interventions." In DIDACTIC TRANSFER OF PHYSICS KNOWLEDGE THROUGH DISTANCE EDUCATION: DIDFYZ 2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0080637.

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Le, Van-Hung, Hai Vu, Thuy Thi Nguyen, Thi-Lan Le, Thi-Thanh-Hai Tran, Michiel Vlaminck, Wilfried Philips, and Peter Veelaert. "3D Object Finding Using Geometrical Constraints on Depth Images." In 2015 Seventh International Conference on Knowledge and Systems Engineering (KSE). IEEE, 2015. http://dx.doi.org/10.1109/kse.2015.17.

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"A novel watermarking scheme against geometrical distortions based on Contourlet transform." In 2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2011). IEEE, 2011. http://dx.doi.org/10.1109/fskd.2011.6019838.

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Haddad, Jane, and Henry Stark. "Image restoration from a geometrical viewpoint." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.ml5.

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In the classical image restoration problem by constrained least-squares, a constraint on the noise variance is combined with a smoothing operation to restore the image and reduce the effect of ill-conditioning. The smoothing operation is not always easy to justify from a physical point of view and therefore has an ad-hoc flavor. We propose an alternative approach to image restoration based on Hilbert space ideas in which the restored image must be at the intersection of sets of vectors that are physically constrained. This approach allows for the incorporation of significant prior knowledge, about both the noise and the signal to be restored. We compare the two approaches analytically and numerically.

Venkata Krishna, K., Neeraj Paul Manelil, and M. P. Maiya. "Geometrical optimization of longitudinal cooling fins for metal hydride based hydrogen storage reactors." In 2021 International Conference on Computational Intelligence and Knowledge Economy (ICCIKE). IEEE, 2021. http://dx.doi.org/10.1109/iccike51210.2021.9410738.

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Ryston, Matěj. "Homemade geometrical models - Teaching general relativity at the secondary school level with activities." In DIDACTIC TRANSFER OF PHYSICS KNOWLEDGE THROUGH DISTANCE EDUCATION: DIDFYZ 2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0078427.

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Coelho, C., M. Straforini, and M. Campani. "Using geometrical rules and a priori knowledge for the understanding of indoor scenes." In British Machine Vision Conference 1990. British Machine Vision Association, 1990. http://dx.doi.org/10.5244/c.4.41.

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Koprowski, Robert, and Zygmunt Wrobel. "Methods for Acquiring Geometrical Properties in an Image Employed for Determining Image Stereo-Correspondence." In 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2008. http://dx.doi.org/10.1109/fskd.2008.553.

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Yao, Jianhua, Joseph E. Burns, Sasha Getty, James Stieger, and Ronald M. Summers. "Automated extraction of anatomic landmarks on vertebrae based on anatomic knowledge and geometrical constraints." In 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI 2014). IEEE, 2014. http://dx.doi.org/10.1109/isbi.2014.6867892.

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Reports on the topic "Geometrical knowledge":

Zhao, Feng. Practical Control Algorithms for Nonlinear Dynamical Systems Using Phase-Space Knowledge and Mixed Numeric and Geometric Computation. Fort Belvoir, VA: Defense Technical Information Center, October 1997. http://dx.doi.org/10.21236/ada330093.

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Zhao, Feng. Practical Control Algorithms for Nonlinear Dynamical Systems Using Phase-Space Knowledge and Mixed Numeric and Geometric Computation. Fort Belvoir, VA: Defense Technical Information Center, September 1998. http://dx.doi.org/10.21236/ada353610.

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Yan, Yujie, and Jerome F. Hajjar. Automated Damage Assessment and Structural Modeling of Bridges with Visual Sensing Technology. Northeastern University, May 2021. http://dx.doi.org/10.17760/d20410114.

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Recent advances in visual sensing technology have gained much attention in the field of bridge inspection and management. Coupled with advanced robotic systems, state-of-the-art visual sensors can be used to obtain accurate documentation of bridges without the need for any special equipment or traffic closure. The captured visual sensor data can be post-processed to gather meaningful information for the bridge structures and hence to support bridge inspection and management. However, state-of-the-practice data postprocessing approaches require substantial manual operations, which can be time-consuming and expensive. The main objective of this study is to develop methods and algorithms to automate the post-processing of the visual sensor data towards the extraction of three main categories of information: 1) object information such as object identity, shapes, and spatial relationships - a novel heuristic-based method is proposed to automate the detection and recognition of main structural elements of steel girder bridges in both terrestrial and unmanned aerial vehicle (UAV)-based laser scanning data. Domain knowledge on the geometric and topological constraints of the structural elements is modeled and utilized as heuristics to guide the search as well as to reject erroneous detection results. 2) structural damage information, such as damage locations and quantities - to support the assessment of damage associated with small deformations, an advanced crack assessment method is proposed to enable automated detection and quantification of concrete cracks in critical structural elements based on UAV-based visual sensor data. In terms of damage associated with large deformations, based on the surface normal-based method proposed in Guldur et al. (2014), a new algorithm is developed to enhance the robustness of damage assessment for structural elements with curved surfaces. 3) three-dimensional volumetric models - the object information extracted from the laser scanning data is exploited to create a complete geometric representation for each structural element. In addition, mesh generation algorithms are developed to automatically convert the geometric representations into conformal all-hexahedron finite element meshes, which can be finally assembled to create a finite element model of the entire bridge. To validate the effectiveness of the developed methods and algorithms, several field data collections have been conducted to collect both the visual sensor data and the physical measurements from experimental specimens and in-service bridges. The data were collected using both terrestrial laser scanners combined with images, and laser scanners and cameras mounted to unmanned aerial vehicles.