Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 21 of 21
Full-Text Articles in Entire DC Network
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.
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.
Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy
Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy
Theses Digitization Project
The purpose of this project is to demonstrate first why trisection for an arbitrary angle is impossible with compass and straightedge and second how trisection does become possible if a marked ruler is used instead.
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.
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.
Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas
Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas
Theses Digitization Project
The purpose fo this project is to study ideals in polynomial rings and affine varieties in order to establish a connection between these two different concepts. Doing so will lead to an in depth examination of Groebner bases. Once this has been defined, step will be outlined that will enable the application of the Groebner Basis Algorithm to geometric problems.
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.
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.
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.
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.
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Theses Digitization Project
The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.
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.
The Riemann Zeta Function, Ernesto Oscar Reyes
The Riemann Zeta Function, Ernesto Oscar Reyes
Theses Digitization Project
The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the functional equation that the the Riemann Zeta Function satisfies.
The Cyclic Cutwidth Of Mesh Cubes, Dwayne William Clarke
The Cyclic Cutwidth Of Mesh Cubes, Dwayne William Clarke
Theses Digitization Project
This project's purpose was to understand the workings of a new theorem introduced in a professional paper on the cutwidth of meshes and then use this knowledge to apply it to the search for the cyclic cutwidth of the n-cube.
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 …
Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun
Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun
Theses Digitization Project
No abstract provided.
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.
A Lower Bound For The Cyclic Cutwidth Of The N-Cube, James Shigeo Namekata
A Lower Bound For The Cyclic Cutwidth Of The N-Cube, James Shigeo Namekata
Theses Digitization Project
No abstract provided.
A Study In Geometric Construction, Nichola Sue Mcclain
A Study In Geometric Construction, Nichola Sue Mcclain
Theses Digitization Project
No abstract provided.
Cyclic Cutwidth Of Three Dimensional Cubes, Ray N. Gregory
Cyclic Cutwidth Of Three Dimensional Cubes, Ray N. Gregory
Theses Digitization Project
No abstract provided.
Analysis On A Hyperplane Of The Quaternions, Pamela Jean Whelchel
Analysis On A Hyperplane Of The Quaternions, Pamela Jean Whelchel
Theses Digitization Project
No abstract provided.