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Articles 1 - 21 of 21
Full-Text Articles in Geometry and Topology
Hyperbolicity Equations For Knot Complements, Christopher Martin Jacinto
Hyperbolicity Equations For Knot Complements, Christopher Martin Jacinto
Theses Digitization Project
This study analyzes Carlo Petronio's paper, An Algorithm Producing Hyperbolicity Equations for a Link Complement in S³. Using the figure eight knot as an example, we will explain how Petronio's algorithm was able to decompose the knot complement of an alternating knot into tetrahedra. Then, using the vertex invariants of these tetrahedra, we will explain how Petronio was able to create hyperbolicity equations.
The Banach-Tarski Paradox, Matthew Jacob Norman
The Banach-Tarski Paradox, Matthew Jacob Norman
Theses Digitization Project
The purpose of this thesis is to establish the history and motivation leading up to the Banach-Tarski Paradox, as well as its proof. This study discusses the early history of set theory as it is documented as well as the necessary basics of set theory in order to further understand the contents within. Set theory not only proved to be for the mathematical at heart but also struck interest into the mind of philosophers, theologians, and logicians.
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
Theses Digitization Project
This project demonstrates how an elliptic curve f defined by invariance under two involutions can be represented by the locus of circumcenters of isosceles triangles in the hyperbolic plane, using inversive model.
Geodesics Of Surface Of Revolution, Wenli Chang
Geodesics Of Surface Of Revolution, Wenli Chang
Theses Digitization Project
The purpose of this project was to study the differential geometry of curves and surfaces in three-dimensional Euclidean space. Some important concepts such as, Curvature, Fundamental Form, Christoffel symbols, and Geodesic Curvature and equations are explored.
The Riesz Representation Theorem For Linear Functionals, Thomas Daniel Schellhous
The Riesz Representation Theorem For Linear Functionals, Thomas Daniel Schellhous
Theses Digitization Project
This study will investigate the Riesz representation theorem for linear functionals in relation to locally compact Hausdorff spaces. Two other theorems that are commonly called "Riesz representation theorem" are the theorem for finite-dimensional inner product spaces and the theorem for Hilbert spaces [BN00], and studying these interesting topics helps us to not only gain a better understanding of how linear functionals interact with vector spaces over which they are defined, but also to see faint threads that hint at a deep connection between the various fields of modern mathematics.
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
Theses Digitization Project
The purpose of the project is to examine the action of the composition of split inversions on the hyperbolic plane, H². The model that is used is the poincoŕe disk.
Using Non-Euclidean Geometry In The Euclidean Classroom, Kelli Jean Wasserman
Using Non-Euclidean Geometry In The Euclidean Classroom, Kelli Jean Wasserman
Theses Digitization Project
This study is designed to explore the ramifications of supplementing the basic Euclidean geometry, with spherical geometry, a non-Eugledian geometry curriculum. This project examined different aspects of the impact of spherical geometry on the high school geometry classroom.
Foundations Of Geometry, Lawrence Michael Clarke
Foundations Of Geometry, Lawrence Michael Clarke
Theses Digitization Project
In this paper, a brief introduction to the history, and development of Euclidean geometry will be followed by a biographical background of David Hilbert, highlighting significant events in his educational and professional life. In an attempt to add rigor to the presentation of geometry, Hilbert defined concepts and presented five groups of axioms that were mutually independent yet compatible, including introducing axioms of congruence in order to present displacement.
Tessellations Of The Hyperbolic Plane, Roberto Carlos Soto
Tessellations Of The Hyperbolic Plane, Roberto Carlos Soto
Theses Digitization Project
In this thesis, the two models of hyperbolic geometry, properties of hyperbolic geometry, fundamental regions created by Fuchsian groups, and the tessellations that arise from such groups are discussed.
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
Theses Digitization Project
This thesis covers improvements on the upperbounds for ropelength of a specific class of algebraic knots.
Minimal Surfaces, Maria Guadalupe Chaparro
Minimal Surfaces, Maria Guadalupe Chaparro
Theses Digitization Project
The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.
Tutte Polynomial In Knot Theory, David Alan Petersen
Tutte Polynomial In Knot Theory, David Alan Petersen
Theses Digitization Project
This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.
Conics In The Hyperbolic Plane, Trent Phillip Naeve
Conics In The Hyperbolic Plane, Trent Phillip Naeve
Theses Digitization Project
An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Theses Digitization Project
The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.
Gauss-Bonnet Formula, Heather Ann Broersma
Gauss-Bonnet Formula, Heather Ann Broersma
Theses Digitization Project
From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.
Hausdorff Dimension, Loren Beth Nemeth
Hausdorff Dimension, Loren Beth Nemeth
Theses Digitization Project
The purpose of this study was to define topological dimension and Hausdorff dimension, Namely metric space theory and measure theory. It was verified that in the sets of elementary geometry, the dimensions agree, while in the case of the fractals, the Hausdorff dimension is strictly larger than the topological dimension.
Investigation Of The Effectiveness Of Interface Constraints In The Solution Of Hyperbolic Second-Order Differential Equations, Paul Jerome Silva
Investigation Of The Effectiveness Of Interface Constraints In The Solution Of Hyperbolic Second-Order Differential Equations, Paul Jerome Silva
Theses Digitization Project
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 …
Constructible Circles On The Unit Sphere, Blaga Slavcheva Pauley
Constructible Circles On The Unit Sphere, Blaga Slavcheva Pauley
Theses Digitization Project
In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.
Knot Theory And Wild Knots, Cherie Annette Reardon
Knot Theory And Wild Knots, Cherie Annette Reardon
Theses Digitization Project
No abstract provided.
Using Symbolic Dynamical Systems: A Search For Knot Invariants, Russell Clark Wheeler
Using Symbolic Dynamical Systems: A Search For Knot Invariants, Russell Clark Wheeler
Theses Digitization Project
No abstract provided.
Torus Embedding And Its Applications, Rick Hung Nguyenhuu
Torus Embedding And Its Applications, Rick Hung Nguyenhuu
Theses Digitization Project
No abstract provided.