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Physical Sciences and Mathematics Commons™
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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett
Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett
Number Theory
No abstract provided.
Descartes Comes Out Of The Closet, Nora E. Culik
Descartes Comes Out Of The Closet, Nora E. Culik
Journal of Humanistic Mathematics
While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central character proves …
Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett
Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett
Number Theory
No abstract provided.
An Introduction To Topology For The High School Student, Nathaniel Ferron
An Introduction To Topology For The High School Student, Nathaniel Ferron
Masters Essays
No abstract provided.
Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon
Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon
USF Tampa Graduate Theses and Dissertations
Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization …
Klein Four Actions On Graphs And Sets, Darren B. Glass
Klein Four Actions On Graphs And Sets, Darren B. Glass
Math Faculty Publications
We consider how a standard theorem in algebraic geometry relating properties of a curve with a (ℤ/2ℤ)2-action to the properties of its quotients generalizes to results about sets and graphs that admit (ℤ/2ℤ)2-actions.
Integrating Non-Euclidean Geometry Into High School, John Buda
Integrating Non-Euclidean Geometry Into High School, John Buda
Honors Thesis
The purpose of this project is to provide the framework for integrating the study of non-Euclidean geometry into a high school math class in such a way that both aligns with the Common Core State Standards and makes use of research-based practices to enhance the learning of traditional geometry. Traditionally, Euclidean geometry has been the only strand of geometry taught in high schools, even though mathematicians have developed several other strands. The non-Euclidean geometry that I focus on in this project is what is known as taxicab geometry. With the Common Core Standards for Math Practice pushing students to “model …
Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden
Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden
Journal of Catholic Education
Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical piazza of Saint Peter's Basilica at Vatican City within Rome, Italy.
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Blake Mellor
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.
Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro
Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro
Theses and Dissertations
Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T3 model, and provide an explicit solution to Einstein's equations.
Normal Surfaces And 3-Manifold Algorithms, Josh D. Hews
Normal Surfaces And 3-Manifold Algorithms, Josh D. Hews
Honors Theses
This survey will develop the theory of normal surfaces as they apply to the S3 recognition algorithm. Sections 2 and 3 provide necessary background on manifold theory. Section 4 presents the theory of normal surfaces in triangulations of 3-manifolds. Section 6 discusses issues related to implementing algorithms based on normal surfaces, as well as an overview of the Regina, a program that implements many 3-manifold algorithms. Finally section 7 presents the proof of the 3-sphere recognition algorithm and discusses how Regina implements the algorithm.