The purpose of this thesis is to examine the arithmetical portion of Theon of Smyrna's work entitled: [Greek title omitted] and to determine its significance in the study of the theory of numbers. The thesis comprises three main parts. The first is a brief introductory discussion of the biography of Theon with an attempt to establish his identity and works. Very little scholarly work has been devoted to Theon; what little could be found was dated for the most part in the second half of the nineteenth century, and in Greek mathematical works his activities have attracted little more than a passing mention. In my introductory chapter I have drawn exclusively from this secondary material. The second part of the study is a literal translation of the appropriate arithmetical section of the work. The third part consists of a commentary amounting to a simple exposition of the mathematical content. In a concluding chapter I have attempted to assign to Theon his place in the history of arithmetic and have given some indications of the reasons for his relative unimportance. / Arts, Faculty of / Classical, Near Eastern and Religious Studies, Department of / Graduate

Made available in DSpace on 2016-03-15T19:44:26Z (GMT). No. of bitstreams: 1 Fabiola Batistin.pdf: 2665857 bytes, checksum: 5f0b4530d5ea6488db5184ff8dc44317 (MD5) Previous issue date: 2014-03-17 / Universidade Presbiteriana Mackenzie / This paper have started from the research collection of the art critic, poet, psychoanalyst, teacher and collector Theon Spanudis and its safeguard upheld on two institutions: Museum of Contemporary Art - MAC/USP and Brazilian Studies Institute - IEB / USP. The collection consisting of 453 frames was partially donated to the MAC / USP in 1979 and concluded only after the death of Spanudis in 1986. The Fund Theon Spanudis of IEB / USP was created with the aim of cataloging the donated literary material (poetry books, manuscripts, texts, exhibition catalogs) for further public consultation. The wealth of material, an unprecedented documentary and little explored in their study resulted in a didactic split into three research areas (the transcendence of art, the artists and brands poetic didactic bias of the collection ) in order to better understand Theon Spanudis collection. The museum education boosted the composition and purpose of a curatorial project uniting the many actions of Theon as a critic, poet and collector. Thus, artists within the collection, poems, excerpts from letters and manuscripts, in order to think of the use of part of the collection as a base material for educational activities inside and outside the art museums were selected: one three-dimensional casts a Poem broad horizon to so many other collections that may incur in the same poetic way. / O presente trabalho partiu da investigação da coleção do crítico de arte, poeta, psicanalista, professor e colecionador Theon Spanudis e de sua salvaguarda acolhida sobre duas instituições: Museu de Arte contemporânea MAC/USP e o Instituto de Estudos Brasileiros IEB/USP. A coleção, composta de 453 quadros, foi doada parcialmente no MAC/USP em 1979 e somente concluída após a morte de Spanudis em 1986. O Fundo de Acervo Theon Spanudis no IEB/USP, foi criado com o intuito de catalogação do material literário doado (livros de poesia, manuscritos, textos, catálogos de exposição) para posterior consulta pública. A riqueza do material, um corpus documental inédito e pouco explorado em seu estudo deram origem a uma separação didática em três eixos de investigação (a transcendência da arte, as marcas poéticas do artistas e o viés didático da coleção) com a finalidade de melhor compreender a Coleção Theon Spanudis. A educação museal impulsionou a composição e a proposta de um projeto curatorial unindo as muitas ações de Theon como crítico, mecenas, poeta, colecionador. Assim, foram selecionados artistas dentro da coleção, poemas, trechos de cartas e de textos manuscritos, com o intuito de pensar o uso de parte da coleção como material de base para ações educativas dentro e fora dos museus de arte: um Poema Tridimensional lança um horizonte amplo a tantas outras coleções que possam incorrer num mesmo caminho poético.

Submitted by (lucia.rodrigues@ufrpe.br) on 2017-03-28T15:03:54Z No. of bitstreams: 1 Danilo Albuquerque de Campos.pdf: 453917 bytes, checksum: 1b07ec11128857b2e96af37543e335fe (MD5) / Made available in DSpace on 2017-03-28T15:03:55Z (GMT). No. of bitstreams: 1 Danilo Albuquerque de Campos.pdf: 453917 bytes, checksum: 1b07ec11128857b2e96af37543e335fe (MD5) Previous issue date: 2014-08-22 / In this work we are interested in showing three algorithms rational approximation of square roots by methods unknown or underutilized by teachers of elementary and secondary education. We begin by defining numerical sequence and convergence of sequences, will discuss the need to expand the concept of rational number and demonstrate the irrationality of the diagonal of a square. Prove an important theorem known in the literature as Dirichlet’s theorem and finally elencaremos three methods of approximating the square roots of natural non-perfect square numbers, very simple to be worked on in the classroom that are rational algorithm aproximção of Hiero of Alexandria, Theon’s Ladder and the Pell-Fermat equation, sende latter discursão fundamental to who will perform on the relationship of the three methods presented. / Neste trabalho estamos interessados em mostrar três algoritmos de aproximação racional de raízes quadradas por métodos pouco utilizados ou desconhecidos pelos professores do ensino fundamental e médio. Iniciaremos definindo sequência numérica e convergência de sequências, discutiremos sobre a necessidade de ampliação do conceito de número racional e demonstraremos a irracionalidade da diagonal de um quadrado. Provaremos um importante Teorema conhecido na literatura como o Teorema de Dirichlet, e por fim elencaremos três métodos de aproximação de raízes quadradas de números naturais não quadrados perfeitos, muito simples de serem trabalhados em sala de aula que são: O algoritmo de aproximação racional de Hierão de Alexandria, A escada de Theon e a Equação de Pell-Fermat, sendo este último fundamental para discussão que iremos realizar sobre a relação dos três métodos apresentados.