Nesta dissertação apresentamos a concepção, implementação e validação de uma proposta para o ensino de transformações geométricas no plano usando o ambiente de geometria dinâmica GeoGebra. A proposta integra Geometria e Arte através da construção de pavimentações do plano e de mosaicos de Escher e foi dirigida para professores do ensino fundamental, tendo como objetivo apresentar uma nova alternativa de trabalho na Geometria escolar e também capacitá-los para o uso de mídias digitais nas suas salas de aula. O trabalho foi desenvolvido dentro dos princípios da Engenharia Didática. Na análise e validação da implementação da proposta tomamos como base a teoria Sócio-Histórica, cuja referência principal é a obra de Vygotsky; também utilizamos o trabalho de Duval sobre registros de representação semiótica no processo de aprendizagem da Matemática. A partir das análises a priori e a posteriori observamos que os professores participantes da oficina, através do uso do GeoGebra, se apropriaram dos princípios da geometria dinâmica e dos conceitos da geometria das transformações. / This work presents the conception, implementation and validation of an experiment to teach geometric transformations in the plane using the dynamic geometry environment GeoGebra. The proposal integrates geometry and art through the construction of tessellations of the plane, including Escher's mosaics, and it was directed to elementary school teachers, aiming to present a new alternative to work with geometry using digital media. The work used the principles of Didactic Engineering and the analysis of the experiment was based on the Socio-Historical theory, whose main reference is the work of Vygotsky and on the work of Duval about registers of semiotic representation in the process of mathematics learning. The analysis a priori and a posteriori showed that the teachers, through the use of GeoGebra, learned the principles of dynamic geometry and the concepts of geometry transformations.

No description available.

This article attempts to establish a relationship between the philosophy of Gilles Deleuze and the artistic productions of M.C.Escher. Thus, we present a discussion on the concepts of representation, simulacra and event, covering the development of these within the Art and Philosophy. We use the artistic productions of Escher to illustrate the appearance of these productions that are on the limit between the definition and the paradox. We believe that both Deleuze as Escher explored this fissure where the paradoxical forces are held in a double sense that never reaches the final term. These thinkers stepped into this space of intensive forces, however, without be engulfed into an abyss undifferentiated. We will use any thoughts available to establish this connection between Escher and Deleuze, so we will use Geometry, Logic, Art and Philosophy, in search of concepts that can help us in this venture. Finally, through this present study we will show Escher as an artist between the geometry and the abysmal forces of abstract art. He sought in his work what he called "espanto" which, in our view, is the same deleuzian discovery of thought without an image. This paradoxical tension that dissipates offering to the spirit an affection that is unrepresentable, a-significant, but at the same time carries all the possible meanings. This element gives us the birth of impossible objects in the fissure existing in compossibility between worlds incompossible. So we try to show how Escher was an artist able to present these elements in their artistic productions. / Este texto procurou estabelecer um agenciamento entre a filosofia de Gilles Deleuze e as produções artísticas de M.C.Escher. Desta forma, apresentamos uma discussão sobre os conceitos de representação, simulacro e acontecimento, percorrendo o desenvolvimento destes dentro da Arte e da Filosofia. Utilizamos as produções artísticas de Escher para ilustrar o aparecimento destas produções que se encontram no limite entre a definição e o paradoxo. Entendemos que tanto Deleuze quanto Escher exploraram esta fissura onde as forças paradoxais se desenrolam em um duplo sentido que nunca chega ao termo final. Estes pensadores adentraram este espaço de forças intensivas sem, no entanto, serem tragados para um abismo indiferenciado. Utilizar-nos-emos de qualquer pensamento disponível para estabelecermos este agenciamento entre Escher e Deleuze, por isso, não nos furtaremos à possibilidade de percorrer a Geometria, a Lógica, a Arte e a Filosofia, em busca de conceitos que possam nos ajudar neste empreendimento. Finalmente, através deste estudo apresentamos Escher como um artista atravessado pelo regramento do geômetra e pelas forças abismais da arte abstrata. Ele em sua obra buscou aquilo que denominou de espanto , que, em nosso entendimento, se refere à mesma descoberta deleuzeana de um pensamento sem imagem. Esta tensão paradoxal que se dissipa oferecendo ao espírito um afeto irrepresentável e asignificante, mas, que ao mesmo tempo carrega consigo todas as significações possíveis. Este elemento apresenta-nos o nascimento dos objetos impossíveis na fissura existente na compossibilidade entre mundos incompossíveis. Assim, procuramos mostrar como Escher foi um artista capaz de apresentar estes elementos em suas produções artísticas. / Mestre em Filosofia

Orientador: Prof. Dr. Armando Caputi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, Santo André, 2018. / Este estudo apresenta as obras do artista holandês M.C.Escher como subsídio ao ensino das isometrias. Suas obras são repletas de movimento, padrões e regularidades, onde as figuras se transformam, se repetem e refletem, fazendo com que o observador seja invariavelmente atraído para descobrir suas particularidades, ou seja, suas simetrias, tornando assim o processo de aprendizagem em algo diferente, concreto e atraente. Após uma breve apresentação das simetrias, conheceremos um pouco sobre Escher e suas obras, abordaremos o conceito de grupo com destaque ao grupo das isometrias com a proposição que identifica a reflexão como unidade básica, afirmando que qualquer que seja a isometria no plano, esta poderá ser obtida pelo produto de, no máximo, três reflexões. Complementando este estudo apresentaremos uma aplicação da teoria das isometrias, através do grupo dos ornamentos, onde podemos observar uma bela relação da matemática à arte. Ao final, algumas sugestões de atividades. / This study presents the works of the Dutch artist M.C.Escher as a subsidy for the learning of isometries. His works are full of movement, patterns and regularities, where the figures are transformed, repeated and reflected, making the observer invariably attracted to discover their particularities, that is, their symmetries, thus making the process of learning in something different, concrete and attractive. After a brief presentation of the symmetries, we will know a little more about Escher¿s works, we will approach the concept of group with emphasis on the group of isometries with the proposition that identifies reflection as basic unit, stating that every isometry in the plane can represented as a product of at most three reflections. Complementing this study we present an application of the isometries theory through the group of ornaments, where we can observe a beautiful connection of mathematics and art. At the end it is presented some suggestions for activities.

The aims of this study were to explore professionals’ and clients’ experiences of diagnosis and treatment of auditory verbal hallucinations with a view to identifying important clinical issues for counselling psychologists. Six professionals, three psychologists and three psychiatrists, who had worked with people who hear voices, alongside four clients who hear voices, volunteered and participated in a semi-structured interview. These interviews were transcribed and analysed using Interpretative Phenomenological Analysis (IPA) as described by Smith, Flowers and Larkin (2009). A table of super-ordinate and sub-ordinate themes was created as a result of this analysis. A number of themes arose from both groups of participants’ experiences. The main themes that arose for the professionals was: professional ambivalence; varying theories on causes of voices; perspectives on diagnosis and formulation; perspectives on medication; thoughts on working therapeutically; and, thinking on recovery. The themes that arose from the clients’ experiences were feelings about diagnosis and experiences of treatment. This research concludes that there is professional ambivalence in working with people who hear voices that is caused by a lack of certainty about the causes of the phenomenon alongside a lack of training in working with clients who have symptoms of psychosis. This impacts clients in several ways. The clients in this study were not offered the option to have any involvement in their own care and none of them were offered therapy as a treatment option. The study also concludes that psychiatric diagnosis does not consider all pertinent information related to clients’ issues which can lead to inconsistency in the diagnosis of clients who hear voices.

Through an exploration of both sculptural and thought processes undertaken in making my Masters exhibition, ‘Hippocampus’, I unpack some possibilities, instabilities, and limitations inherent in representation and visual perception. This thesis explores the Hippocampus as image (seahorse) and concept (brain-structure involved in cognitive mapping of space). Looking at Gilles Deleuze’s writings on representation, I will expand on the notion of the map as being that which does not define and fix a structure or meaning, but rather is open, extendable and experimental. I explore the becoming, rather than the being, of image and concept. The emphasis here is on process, non-representation, and fluidity of meaning. This is supportive of my personal affirmation of the practice and process of art-making as research. I will refer to the graphic prints of Maurits Cornelis Escher as a means to elucidate a visual contextualization of my practical work, particularly with regard to the play with two- and three-dimensional space perception. Through precisely calculated ‘experiments’ that show up the partiality of our visual perception of space, Escher alludes to things that either cannot actually exist as spatial objects or do exist, but resist representation. Similarly I will explore how my own sculptures, although existing in space resist a fixed representation and suggest ideas of other spaces, non-spaces; an in-between space that does not pin itself down and become fixed to any particular image, idea, objector representation.

ABSTRACT And concrete diction Carl Jonas Love Almqvist’s Drottningens juvelsmycke (The Queen's Tiara; 1834) is, along with Amorina, the work primarily associated with the ”poetic fugue” – a concept the author develops in ”Om enheten av epism och dramatism; en aning om den poetiska fugan” (”On the unity of epism and dramatism; a notion of the poetic fugue”; 1821); an essay often considered vague and theoretical by researchers in the field. The meaning of the poetic fugue has been regarded unclear, but mainly considered as some kind of synthesis of epic and dramatic writing. This essay argues that that is not the case, and that this one-dimensional approach both limits the interpretations of the essay and the poetic fugue as a whole. From a multidisciplinary perspective, with myself and my own reader as a part of the fugue itself, the aim of this essay is to highlight a very important overseen aspect of the poetic fugue, and Almqvist’s writing in general – the connections to mathematics, the analogies between abstract and concrete levels, and how these are deeply intertwined. The results in this essay are derived from a close reading technique based on mathematical problem solving called the ideotic method (den ideotiska metoden), and analyzed with Douglas Hofstadter's theory of Strange loops in Gödel, Escher, Bach – an eternal golden braid (1979). This analysis shows that this analogy is not just about the composition of a poetic piece of art, a synthesis of epic and dramatic writing, or the relation between music and text. Instead the results do point to an alternative interdisciplinary interpretation, where the relations between parts and units, realities and fictions, readers and texts, make the poetic fugue more of an analogy for the universe as a whole – a living and breathing ”animal coeleste” in contrast to the Newtonian ”mechanical coeleste”. An analogy which, thanks to its mathematical construction and way of looking at time as non-linear, is connected to both Einstein’s theory of relativity and quantum theory – the science of the very big and the very small, parts and units, of everything, including ourselves.