Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.) -- Central Connecticut State University, 2009. / Title from electronic title page. Project advisor: Adele Miller. "A special project submitted in partial fulfillment of the requirements for the degree of Master of Science in Secondary Mathematics Education." Includes bibliographical references.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2005. / Includes bibliographical references.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (p. 51).

Thesis (Ph. D.)--University of Montana, 2007. / Title from title screen. Description based on contents viewed July 19, 2007. Includes German text: Geometrische Untersuchungen zur Theorie der Parallellinien / von Nicolaus Lobatschewsky. Includes bibliographical references (p. 279-282).

The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral structure of this tropicalization and calculate the fibers of the tropicalization map. Using a recent result of Gubler, Rabinoff, and Werner, we prove that there is a continuous section of the tropicalization map.

Orientador: Claudina Izepe Rodrigues / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T10:14:12Z (GMT). No. of bitstreams: 1 Oliveira_VivianneTassoPeruginide_M.pdf: 42677277 bytes, checksum: e029738b1504da7dbb6995d59c3b35f5 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho apresentamos o estudo sobre a Geometria do Táxi, uma Geometria não-Euclidiana de fácil compreensão e muito próxima do cotidiano das pessoas, uma vez que tem uma ampla gama de aplicações em situações relacionadas à geografia urbana. A Geometria do Táxi é uma geometria muito semelhante à Geometria Euclidiana, diferindo desta apenas pela definição de distância. Enquanto que, na Geometria Euclidiana, a distância entre dois pontos é o comprimento do segmento de reta que os une, podendo ser obtida com o auxílio do Teorema de Pitágoras, na Geometria do Táxi, a distância entre dois pontos é o comprimento do menor caminho percorrido por linhas horizontais e verticais de um ponto a outro. Esse pequeno detalhe sob o ponto de vista matemático, apresenta grandes diferenças, principalmente nas figuras geométricas que estão relacionadas à distância. Abordamos esse aspecto sob a forma de exemplos e apresentamos no final do trabalho uma sugestão de atividades pedagógicas para serem trabalhadas em sala de aula / Abstract: In this paper we present the study of the Taxicab Geometry, a non-Euclidean Geometry of easy understanding and very close to people's daily lives, as it has a wide range of applications in situations related to urban geography. The Taxicab Geometry is a geometry very similar to Euclidian Geometry, differing only by the definition of distance. While in Euclidean Geometry the distance between two points is the length of the line that unites them, which can be obtained with the help of the Pythagorean Theorem, in the Taxicab Geometry the distance between two points is the length of the shortest path travelled by horizontal and vertical lines from one point to another. This small detail, from the mathematical point of view, presents major differences, particularly in the geometric figures that are related to distance. We cover this aspect in the form of examples and present in the end of the work a suggestion of pedagogical activities to be used in class / Mestrado / Matemática em Rede Nacional / Mestra em Matemática em Rede Nacional

The purpose of this paper is to investigate some of the properties of convex sets in the plane through synthetic geometry.

Solutions to differential equations describing the behavior of physical quantities (e.g., displacement, temperature, electric field strength) often only have finite range of validity over a subdomain. Interest beyond the subdomain often arises. As a result, the problem of making the solution compatible across the connecting subdomain interfaces must be dealt with. Four different compatibility methods are examined here for hyperbolic (time varying) second-order differential equations. These methods are used to match two different solutions, one in each subdomain along the connecting interface. The entire domain that is examined here is a unit square in the Cartesian plane. The four compatibility methods examined are: point collocation; optimal least square fit; penalty function; Ritz-Galerkin weak form. Discretized L2 convergence is used to examine and compare the effectiveness of each method.

Euclid’s Method of finding Pythagorean triples is a commonly accepted and applied technique. This study focuses on a myriad of other methods behind finding such Pythagorean triples. Specifically, we discover whether or not other ways of finding triples are special cases of Euclid’s Method.