[pt] A presente dissertação analisa a relação interdisciplinar entre a matemática e as artes, dando especial destaque ao Teorema de Desargues como uma ponte entre estas áreas. Destaca-se a importância atual da interdisciplinaridade na educação, embasada pela Base Nacional Comum Curricular (BNCC), que dá destaque à integração de tecnologia e conhecimento em múltiplas áreas do currículo escolar. O Teorema de Desargues é abordado como um conceito que rompe os limites da matemática, alcançando também os campos da arte e da tecnologia. A Geometria Projetiva é contextualizada historicamente, apresentando seus primeiros passos e progresso ao longo do tempo. Revela Girard Desargues como um como precursor de ideias nesse contexto, contribuindo tanto para o avanço da matemática quanto para a expressão artística. A dissertação enfatiza a aplicação prática do Teorema de Desargues no contexto educacional, propondo atividades significativas e atrativas para os alunos no contexto escolar. Apresenta o produto educacional desenvolvido pelos autores como uma fonte valiosa de sugestões para educadores que pretendem se dedicar à interdisciplinaridade. A dissertação promove uma abordagem educacional que estimula o diálogo entre disciplinas, destacando a conexão entre matemática, geometria projetiva, arte e tecnologia, para isso utiliza o Teorema de Desargues desempenhando um papel central nesse processo. / [en] The present dissertation examines the interdisciplinary relationship between mathematics and the arts, with special emphasis on Desargues Theorem as a bridge between these fields. It highlights the current importance of interdisciplinarity in education, supported by the National Common Curricular Base (BNCC), which emphasizes the integration of technology and knowledge across multiple areas of the school curriculum. Desargues Theorem is approached as a concept that transcends the boundaries of mathematics, also reaching into the realms of art and technology. Projective Geometry is historically contextualized, tracing its origins and development over time. Girard Desargues is revealed as a precursor of ideas in this context, contributing to both the advancement of mathematics and artistic expression. The dissertation emphasizes the practical application of Desargues Theorem in the educational context, proposing meaningful and engaging activities for students in the school setting. It presents the educational product developed by the authors as a valuable source of suggestions for educators looking to dedicate themselves to interdisciplinarity. The dissertation promotes an educational approach that encourages dialogue between disciplines, highlighting the connection between mathematics, projective geometry, art, and technology, utilizing Desargues Theorem as a central element in this process.

Yes / The Desargues property is well known in the context of projective geometry. An analogous property is presented in the context of both classical and Quantum Physics. In a classical context, the Desargues property implies that two logical circuits with the same input, show in their outputs selective correlations. In general their outputs are uncorrelated, but if the output of one has a particular value, then the output of the other has another particular value. In a quantum context, the Desargues property implies that two experiments each of which involves two successive projective measurements, have selective correlations. For a particular set of projectors, if in one experiment the second measurement does not change the output of the rst measurement, then the same is true in the other experiment.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-08T15:28:34Z No. of bitstreams: 1 divaneaparecidademoraesdantas.pdf: 855862 bytes, checksum: e55bbef7c7060caa2ff49488eb611852 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T13:29:55Z (GMT) No. of bitstreams: 1 divaneaparecidademoraesdantas.pdf: 855862 bytes, checksum: e55bbef7c7060caa2ff49488eb611852 (MD5) / Made available in DSpace on 2016-07-13T13:29:55Z (GMT). No. of bitstreams: 1 divaneaparecidademoraesdantas.pdf: 855862 bytes, checksum: e55bbef7c7060caa2ff49488eb611852 (MD5) Previous issue date: 2012-03-08 / O principal objetivo do trabalho é estudar os Espaços de Moduli das Configurações de Desargues, e este estudo é baseado no artigo (AVRITZER; LANGE, 2002). Uma configuração de 10 pontos e 10 retas, chamada uma configuração 103,obtidas do clássico teorema de Desargues, é chamada uma configuração de Desargues. Muitos espaços de moduli, senão todos, são obtidos algebricamente através das variedades algébricas de quociente, por isso estudamos um pouco de Teoria Geométrica dos Invariantes, ações de grupos algébricos em variedades algébricas e mostramos que existe o quociente categórico de uma variedade algébrica X por um grupo finito G e quando ele é o espaço e moduli grosso. Além disso mostramos que quando a variedade algébrica é afim (resp. quase projetiva) o quociente categórico é uma variedade algébrica afim (resp. quase projetiva). Finalmente, provamos que o quociente categórico(MD,p) de ˇP3 pelo grupo finito S5 é o espaço de moduli grosso para as configurações de Desargues. / The main aim of this work is to study the moduli space of Desargues configurations and it was based in (AVRITZER; LANGE, 2002). A configurations of 10 points and 10 line of the classic Desargues Theorem is called a Desargues configuration. Many moduli spaces, if not all, are obtained algebraically through the quotient of algebraic varieties. So we have studied a little about Geometric Invariant Theory and actions of algebraic group on varieties. We have showed that there exist the categorical quotient of a algebraic variety X by a finite algebraic group G and that it is a coarse moduli space. Moreover, we have showed that if X is a affine (resp. quasi-projective) the categorical quotient is an affine (resp. quasi-projective) variety Finally, we proved that the categorical quotient (MD,p) of the ˇP3 by the algebraic group finite S5 is the moduli space coarse for the Desargues configurations.

Submitted by Douglas Gonçalves Leite (dgllpk@hotmail.com) on 2018-07-12T19:45:59Z No. of bitstreams: 1 Dissertação de Mestrado Douglas Gonçalves Leite.pdf: 3637073 bytes, checksum: 862cfe8465504cabc78dc9fa4b76982f (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-07-13T13:49:00Z (GMT) No. of bitstreams: 1 leite_dg_me_rcla.pdf: 3570557 bytes, checksum: 9797dab228f3bf66569d69ce53ed6b1e (MD5) / Made available in DSpace on 2018-07-13T13:49:00Z (GMT). No. of bitstreams: 1 leite_dg_me_rcla.pdf: 3570557 bytes, checksum: 9797dab228f3bf66569d69ce53ed6b1e (MD5) Previous issue date: 2018-05-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho discorre a respeito de dois textos do arquiteto e matemático francês Girard Desargues. As obras que aqui chamamos de Método de Perspectiva (1636) e Brouillon Project (1639), foram desenvolvidas em um período com ampla produção teórica relacionada a técnicas de representação. No trabalho de 1636 Desargues descreveu o processo necessário para representar uma gaiola em perspectiva. No trabalho, Brouillon Project, ele trata de propriedades geométricas envolvendo feixe de retas aproximando-se dos conceitos existentes no campo das projeções de figuras, contudo parte das referências utilizadas, como Chasles, Poudra, Taton, entre outros, consideraram que o Brouillon Project foi um trabalho relacionado as seções cônicas. Nosso objetivo é apresentar uma análise envolvendo os conteúdos geométricos explorados nas duas obras citadas com o intuito de relacioná-las com o campo da perspectiva e projeção de figuras. Para isso, desenvolvemos uma pesquisa em história da matemática envolvendo história perspectiva, história da geometria, forma de produção do conhecimento daquele período, em conjunto com teorias que estavam sendo produzidas até o séc. XVII. / The present work deals with two texts of the French architect and mathematician Girard Desargues. The works that we call the Method of Perspective (1636) and Brouillon Project (1639) were developed in a period with a large theoretical production related to representations of figures in perspective. In the work of 1636 Desargues described the process necessary to represent a cage in perspective. At work, Brouillon Project, he dealt with geometric properties involving beam of straight lines approaching the existing concepts in the field of projections of figures. However, some of the references used, such as Chasles, Poudra, Taton, and others, consider that the Brouillon Project was a work related to the conic sections. Our objective is to present a study involving the geometric contents explored in the two works mentioned, seeking to relate them to the field of perspective and projection of figures. For this, we developed a research in history of mathematics involving history, perspective, history of geometry, form of knowledge production of that period, together with theories that were being produced until the century. XVII.

Girard Desargues (1951-1662) was a key figure in the transformation of architectural geometry from its ancient and venerated status as transcendental knowledge and supreme reality to a mere technological instrument for the control of building construction practice. As a friend of Rene Descartes and Marin Mersenne, Desargues participated in the development of the mechanistic worldview which accompanied the emergence of experimental science and the renewed interest in mathematics and geometry as axiomatic, deductive systems. This dissertation examines in detail Desargues' methods of stereotomy (the geometrical basis of architectural stone cutting) and his system of perspective construction without vanishing points beyond the picturespace. Desargues' theorem and other key discoveries for which he is still known in the history of mathematics are discussed as they bear upon his methods of stereotomy and perspective. Desargues' stereotomy is almost certainly the first attempt at a universal descriptive geometry such as Gaspard Monge finally developed after the French revolution. Desargues' work in this area may thus be seen as a precocious foreshadowing of the engineering geometry in common use today. The writings of Desargues have been consulted in the original French. Extensive passages are quoted and translated, and a number of illustrations from the original texts are reproduced. Supplementary illustrations are also provided. Appendices list the known architectural works of Desargues, his writings and those of his friend and student Bosse which bear upon the exposition of Desargues' methods. / Ph. D.

Submitted by Lúcia Brandão (lucia.elaine@live.com) on 2015-12-11T20:13:50Z No. of bitstreams: 1 Dissertação - Yury dos Santos Bezerra.pdf: 12355510 bytes, checksum: 71b4c028c620d01d7b179abec5d64207 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2016-01-19T18:12:54Z (GMT) No. of bitstreams: 1 Dissertação - Yury dos Santos Bezerra.pdf: 12355510 bytes, checksum: 71b4c028c620d01d7b179abec5d64207 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2016-01-19T18:25:08Z (GMT) No. of bitstreams: 1 Dissertação - Yury dos Santos Bezerra.pdf: 12355510 bytes, checksum: 71b4c028c620d01d7b179abec5d64207 (MD5) / Made available in DSpace on 2016-01-19T18:25:08Z (GMT). No. of bitstreams: 1 Dissertação - Yury dos Santos Bezerra.pdf: 12355510 bytes, checksum: 71b4c028c620d01d7b179abec5d64207 (MD5) Previous issue date: 2014-11-21 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of the present work, analyze the main theorems of projective geometry, presenting some problems and their solutions, using the Menelaus theorem and some arguments of classical geometry. Even if it is unknown to the students Teaching Average, the aim of this work was to present it to them through the introduction of knowledge this fundamental geometry, as Projetividade, perspectivity, dual loved and some theorems as the Desargues' theorem, the fundamental theorem and the theorem of Pappus. Expected that through this approach on some basic applications of projective geometry, are proportionate conditions necessary for the reader, professors and experts deepen their knowledge of projective geometry and be motivated to continue to research the subject at hand and motivate them to seek other sources of information to facilitate advances the re fl ections of this geometry. It is expected also that the teacher can arouse the interest of his students by research on this very important geometry in our lives. / Objetivou-se, com o presente trabalho, analisar os principais teoremas da Geometria Projetiva, apresentando alguns problemas e suas respectivas soluções, recorrendo ao teorema de Menelaus e alguns argumentos da Geometria Clássica. Mesmo sendo ela desconhecida pelos alunos do Ensino Médio, busca-se com este trabalho apresentá-la a eles por meio da introdução de conhecimentos fundamentais desta geometria, como Projetividade, Perspectividade, entes duais e alguns teoremas como: o Teorema de Desargues, o Teorema Fundamental e o Teorema de Pappus. Espera-se que através desta abordagem sobre algumas aplicações básicas da Geometria Projetiva, sejam proporcionadas condições necessárias para que o leitor, professores e especialistas aprofundem seus conhecimentos sobre a Geometria Projetiva e se sintam motivados para continuar a pesquisar o assunto em pauta,bem como os motive a buscar outras fontes de informações para favorecer avanços nas reflexões desta geometria. Espera-se, ainda, que o professor possa despertar o interesse dos seus alunos pela pesquisa sobre esta geometria muito importante na nossa vida.

This diploma thesis is focused on Selected problems in planimetry. The aim of this diploma thesis is description not only planimetric problems and their verification in a dynamic mathematical program GeoGebra, but also presentation of the author after whom it is called. The thesis is illustrated with pictures, which can help the reader to understand the problem and verification. This thesis can be used as a supplement the curriculum in secondary schools, where using dynamic program GeoGebra and subsequent verification may reach a better understanding of the topic.