Projective Geometry Hidden Inside: Can You Spot It?, 2016 Dordt College
Projective Geometry Hidden Inside: Can You Spot It?, Tom Clark
Faculty Work Comprehensive List
In this talk Dr. Clark shared about a Math Teachers’ Circle session he recently ran centered around the children’s game Spot it! This game has some very interesting mathematics behind it and naturally begs to be explored with inquiry. He described the way he led teachers to ask questions about the game, the way the teachers then explored the topic, and the mathematics behind it all.
Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, 2016 The University of Western Ontario
Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega
Electronic Thesis and Dissertation Repository
Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this thesis we use elliptic theory for edge- degenerate differential operators on singular manifolds to study general deformations of special Lagrangian submanifolds with edge singularities. We obtain a general theorem describing the local structure of the moduli space. When the obstruction space vanishes the moduli space is a smooth, finite dimensional manifold.
Ε-Kernel Coresets For Stochastic Points, 2016 Utah State University
Ε-Kernel Coresets For Stochastic Points, Haitao Wang, Lingxiao Huang, Jian Li, Jeff Mark Phillips
Computer Science Faculty and Staff Publications
With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over such data. In this paper, we initiate the study of constructing epsilon-kernel coresets for uncertain points. We consider uncertainty in the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location. An epsilon-kernel coreset approximates the width of a point set in any direction. We consider approximating the …
Bridge Spectra Of Cables Of 2-Bridge Knots, 2016 University of Nebraska-Lincoln
Bridge Spectra Of Cables Of 2-Bridge Knots, Nicholas John Owad
Department of Mathematics: Dissertations, Theses, and Student Research
We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.
Advisors: Mark Brittenham and Susan Hermiller
Patterns Formed By Coins, 2016 Formlabs
Patterns Formed By Coins, Andrey M. Mishchenko
Journal of Humanistic Mathematics
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non- overlapping circles. The first half of the article is an exposition of the two most important facts about circle packings, (1) that essentially whatever pattern we ask for, we may always arrange circles in that pattern, and (2) that under simple conditions on the pattern, there is an essentially unique arrangement of circles in that pattern. In the second half of the article, we consider related questions, but where we …
Unfolding Convex Polyhedra Via Radially Monotone Cut Trees, 2016 Smith College
Unfolding Convex Polyhedra Via Radially Monotone Cut Trees, Joseph O'Rourke
Computer Science: Faculty Publications
A notion of "radially monotone" cut paths is introduced as an effective choice for finding a non-overlapping edge-unfolding of a convex polyhedron. These paths have the property that the two sides of the cut avoid overlap locally as the cut is infinitesimally opened by the curvature at the vertices along the path. It is shown that a class of planar, triangulated convex domains always have a radially monotone spanning forest, a forest that can be found by an essentially greedy algorithm. This algorithm can be mimicked in 3D and applied to polyhedra inscribed in a sphere. Although the algorithm does …
Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces (Corrected), 2016 Rose-Hulman Institute of Technology
Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces (Corrected), Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
Two Riemann surfaces S1 and S2 with conformal G-actions have topologically equivalent actions if there is a homeomorphism h : S1 -> S2 which intertwines the actions. A weaker equivalence may be defined by comparing the representations of G on the spaces of holomorphic q-differentials Hq(S1) and Hq(S2). In this note we study the differences between topological equivalence and Hq equivalence of prime cyclic actions, where S1/G and S2/G have genus zero.
The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, 2016 New Mexico State University
The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder
Geometry
No abstract provided.
Pythagorean Combinations For Lego Robot Building., 2016 Loyola University Chicago
Pythagorean Combinations For Lego Robot Building., Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
This paper provides tips for LEGO robot construction involving bracing or gear meshing along a diagonal using standard Botball kits.
Cohomology Of Certain Polyhedral Product Spaces, 2016 Graduate Center, City University of New York
Cohomology Of Certain Polyhedral Product Spaces, Elizabeth A. Vidaurre
Dissertations, Theses, and Capstone Projects
The study of torus actions led to the discovery of moment-angle complexes and their generalization, polyhedral product spaces. Polyhedral products are constructed from a simplicial complex. This thesis focuses on computing the cohomology of polyhedral products given by two different classes of simplicial complexes: polyhedral joins (composed simplicial complexes) and $n$-gons. A homological decomposition of a polyhedral product developed by Bahri, Bendersky, Cohen and Gitler is used to derive a formula for the case of polyhedral joins. Moreover, methods from and results by Cai will be used to give a full description of the non-trivial cup products in a real …
Quaternion Algebras And Hyperbolic 3-Manifolds, 2016 Graduate Center, City University of New York
Quaternion Algebras And Hyperbolic 3-Manifolds, Joseph Quinn
Dissertations, Theses, and Capstone Projects
I use a classical idea of Macfarlane to obtain a complex quaternion model for hyperbolic 3-space and its group of orientation-preserving isometries, analogous to Hamilton’s famous result on Euclidean rotations. I generalize this to quaternion models over number fields for the action of Kleinian groups on hyperbolic 3-space, using arithmetic invariants of the corresponding hyperbolic 3-manifolds. The class of manifolds to which this technique applies includes all cusped arithmetic manifolds and infinitely many commensurability classes of cusped non-arithmetic, compact arithmetic, and compact non-arithmetic manifolds. I obtain analogous results for actions of Fuchsian groups on the hyperbolic plane. I develop new …
General Relativity And Differential Geometry, 2016 Union College - Schenectady, NY
An Investigation Of Minimal Surfaces In So(3), 2016 Rose-Hulman Institute of Technology
An Investigation Of Minimal Surfaces In So(3), Luke Bohn
Rose-Hulman Undergraduate Research Publications
Classical minimal surface theory can be thought of as dealing with the shapes of soap films stretched across wires in Euclidean space R3. This article will examine such structures in an abstract three-dimensional space, the Lie Group SO(3). This is the space of possible rotations in R3, where each rotation is expressed as three angles: two to indicate the axis of rotation and one to indicate the amount of rotation. The properties of the space SO(3) may result in minimal surfaces that behave differently than they do in R3.
Sequences Of Spiral Knot Determinants, 2016 James Madison University
Sequences Of Spiral Knot Determinants, Ryan Stees
Senior Honors Projects, 2010-2019
Spiral knots are a generalization of the well-known class of torus knots indexed by strand number and base word repetition. By fixing the strand number and varying the repetition index we obtain integer sequences of spiral knot determinants. In this paper we examine such sequences for spiral knots of up to four strands using a new periodic crossing matrix method. Surprisingly, the resulting sequences vary widely in character and, even more surprisingly, nearly every one of them is a known integer sequence in the Online Encyclopedia of Integer Sequences. We also develop a general form for these sequences in terms …
Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, 2016 Morehead State University
Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus
Celebration of Student Scholarship Poster Sessions Archive
No abstract provided.
Mathematics And Origami; Unfolding Mathematical "Impossibilities", 2016 Morehead State University
Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams
Celebration of Student Scholarship Poster Sessions Archive
No abstract provided.
The Conway Polynomial And Amphicheiral Knots, 2016 University of Tennessee - Knoxville
The Conway Polynomial And Amphicheiral Knots, Vajira Asanka Manathunga
Doctoral Dissertations
The Conant's conjecture [7] which has foundation on the Conway polynomial and Vassiliev invariants is the main theme of this research. The Conant's conjecture claim that the Conway polynomial of amphicheiral knots split over integer modulo 4 space. We prove Conant's conjecture for amphicheiral knots coming from braid closure in certain way. We give several counter examples to a conjecture of A. Stoimenow [32] regarding the leading coefficient of the Conway polynomial. We also construct integer bases for chord diagrams up to order 7 and up to order 6 for Vassiliev invariants. Finally we develop a method to extract integer …
Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, 2016 University of Tennessee - Knoxville
Non-Compact Solutions To Inverse Mean Curvature Flow In Hyperbolic Space, Brian Daniel Allen
Doctoral Dissertations
We investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over horospheres in Hyperbolic space and show long time existence of the flow as well as asymptotic convergence to horospheres. Along the way many important local estimates as well as global estimates are obtained. In addition, we develop a useful family of cutoff functions for IMCF as well as a non-compact ODE maximum principle at infinity which are integral tools used throughout the document.
Duality Of Scales, 2016 University of Tennessee - Knoxville
Duality Of Scales, Michael Christopher Holloway
Doctoral Dissertations
We establish an interaction between the large scale and small scale using two types of maps from large scale spaces to small scale spaces. First we use slowly oscillating maps, which can be described as those having arbitrarily small variation at infinity. These lead to a Galois connection between certain collections of large scale structures and small scale structures on a given set. Slowly oscillating functions can also be used to define to the notion of a dual pair of scale structures on a space. A dual pair consists of a large and a small scale structure on a space …
Drawing Numbers And Listening To Patterns, 2016 Georgia Southern University
Drawing Numbers And Listening To Patterns, Loren Zo Haynes
Honors College Theses
The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …