Implícits filosòfics del convencionalisme en la geometria espaciotemporal

Treball que té com a objectiu, en primer lloc, establir quina possibilitat té el convencionalisme de ser una alternativa a les concepcions realistes de la geometria relativista; en segon lloc, assenyalar les implicacions epistemològiques que en deriven; en tercer lloc, precisar quin tipus de lectura de la hipòtesi inicial hem de fer donat que hi ha un cert marge per a l’ambigüitat i això ha permès diverses propostes; i en quart i darrer lloc, en cas que hom accepti les restriccions que el convencionalisme imposa al nostre coneixement, hem de veure quines conclusions podem extreure en l’àmbit ontològic i fins a quin punt són significatives per a la discussió sobre la relació entre matemàtica i naturalesa

Elements of Non-Euclidean geometry ...

Mode of access: Internet.

The elements of non-Euclidean geometry,

Mode of access: Internet.

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

La geometria non-euclidea : esposizione storico-critica del suo sviluppo.

Available on demand as hard copy or computer file from Cornell University Library.

Os fractais no urbanismo

Dissertação para obtenção do grau de Mestre em Arquitectura com Especialização em Urbanismo, apresentada na Universidade de Lisboa - Faculdade de Arquitectura.

Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

Treatment of PET and PU polymers by atmospheric pressure plasma generated in dielectric barrier discharge in air

Plasma treatments are frequently employed to modify surface properties of materials such as adhesivity, hydrophobicity, oleophobicity etc. Present work deals with surface modification of common commercial polymers such as polyethylene terephthalate (PET) and polyurethane (PU) by an air dielectric barrier discharge (DBD) at atmospheric pressure. The DBD treatment was performed in a plain reactor in wire-duct geometry (non-uniform field reactor), which was driven by a 60 Hz power supply. Material characterization was carried out by water contact angle measurements, atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). The plasma-induced modifications are associated with incorporation of polar oxygen and nitrogen containing groups on the polymer surface. The AFM analysis reveals that the plasma treatment roughens the material surface. Due to these structural and morphological changes the surface of DBD-treated polymers becomes more hydrophilic resulting in enhanced adhesion properties. (C) 2010 Elsevier B.V. All rights reserved.

Uma introdução à geometria esférica

Pós-graduação em Matemática em Rede Nacional - IBILCE

Um estuo dos modelos da geometria hiperbólica

Pós-graduação em Matemática Universitária - IGCE

Fundamentos de geometria hiperbólica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Über die Picard'schen gruppen aus dem zahlkörper der dritten und der vierten einheitswurzel ...

Available on demand as hard copy or computer file from Cornell University Library.

Die nicht-euklidischen Raumformen in analytischer Behandlung,

Available on demand as hard copy or computer file from Cornell University Library.

Il parallelismo de Clifford negli spazii ellittici.

"Estratto dagli Annali della R. Scuola Normale Superiore di Pisa, v. 9."