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
CUNY Graduate Center
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
CUNY Graduate Center
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 …
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.
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 …
The Cantor Set Before Cantor,
2016
Ursinus College
The Cantor Set Before Cantor, Nicholas A. Scoville
Topology
A special construction used in both analysis and topology today is known as the Cantor set. Cantor used this set in a paper in the 1880s. Yet it appeared as early as 1875 in a paper by the Irish mathematician Henry John Stephen Smith (1826 - 1883). Smith, who is best known for the Smith normal form of a matrix, was a professor at Oxford who made great contributions in matrix theory and number theory. In this project, we will explore parts of a paper he wrote titled On the Integration of Discontinuous Functions.
Topology From Analysis,
2016
Ursinus College
Topology From Analysis, Nicholas A. Scoville
Topology
Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn't this just a distinction without a difference? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis.
Connecting Connectedness,
2016
Ursinus College
The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem,
2016
New Mexico State University
The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder
Geometry
No abstract provided.
Coding Strategies, The Choquet Game And Domain Representability,
2016
University of Dayton
Coding Strategies, The Choquet Game And Domain Representability, Lynne Yengulalp
Mathematics Faculty Publications
We prove that if the NONEMPTY player has a winning strategy in the strong Choquet game on a regular space X then NONEMPTY has a winning coding strategy in that game (a strategy that only depends on the previous 2 moves). We also prove that any regular domain representable space is generalized subcompact.
Domain Representability And Topological Completeness,
2016
University of Dayton
Domain Representability And Topological Completeness, Matthew D. Devilbiss
Honors Theses
Topological completeness properties seek to generalize the definition of complete metric space to the context of topologies. Chapter 1 gives an overview of some of these properties. Chapter 2 introduces domain theory, a field originally intended for use in theoretical computer science. Finally, Chapter 3 examines how this computer-scientific notion can be employed in the study of topological completeness in the form of domain representability. The connections between domain representability and other topological completeness properties are subsequently examined.
Area And Volume Where Do The Formulas Come From?,
2016
John Carroll University
Area And Volume Where Do The Formulas Come From?, Roger Yarnell
Masters Essays
No abstract provided.
Conjugacy Geodesics In Coxeter Groups,
2016
University of Nebraska-Lincoln
Conjugacy Geodesics In Coxeter Groups, Aaron Calderon
UCARE: Research Products
Take a square and flip it over the vertical axis, rotate it 90 degrees counterclockwise and then flip it again over the vertical axis. This sequence is the same as a 90 degree clockwise rotation but takes more steps to demonstrate the same symmetry. In general, the question of when a sequence of symmetries has minimal length is hard to answer and is dependent on the chosen generating set (in our toy example, rotation by 90 degrees and reflection). By realizing sequences of symmetries as paths in a group's Cayley graph, the problem becomes one about the set of shortest …
The Geometry Of Spacetime And Its Singular Nature,
2016
University of Connecticut
The Geometry Of Spacetime And Its Singular Nature, Filip Dul
Honors Scholar Theses
One hundred years ago, Albert Einstein revolutionized our understanding of gravity, and thus the large-scale structure of spacetime, by implementing differential geometry as the pri- mary medium of its description, thereby condensing the relationship between mass, energy and curvature of spacetime manifolds with the Einstein field equations (EFE), the primary compo- nent of his theory of General Relativity. In this paper, we use the language of Semi-Riemannian Geometry to examine the Schwarzschild and the Friedmann-Lemaˆıtre-Robertson-Walker met- rics, which represent some of the most well-known solutions to the EFE. Our investigation of these metrics will lead us to the problem of …
Experimental Demonstration Of Topological Effects In Bianisotropic Metamaterials,
2016
Australian National University
Experimental Demonstration Of Topological Effects In Bianisotropic Metamaterials, Alexey P. Slobozhanyuk, Alexander B. Khanikaev, Dmitry S. Filonov, Daria A. Smirnova, Andrey E. Miroshnichenko, Yuri S. Kivshar
Publications and Research
Existence of robust edge states at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, a topological insulator. Such nontrivial states were originally predicted and discovered in condensed matter physics, but they find their counterparts in other fields of physics, including the physics of classical waves and electromagnetism. Here, we present the first experimental realization of a topological insulator for electromagnetic waves based on engineered bianisotropic metamaterials. By employing the near-field scanning technique, we demonstrate experimentally the topologically robust propagation of electromagnetic waves around sharp corners without backscattering effects.
A New 12-Puzzle,
2016
Butler University
A New 12-Puzzle, Todd Estroff, Jeremiah Farrell
Scholarship and Professional Work - LAS
This puzzle is a continuation of the tribute to the magician Paul Swinford. The following 18 two-letter words use each of the 12 letters of PAUL SWINFORD exactly three times each. The words are to be placed on the nodes of the grid so that each hexagon and each of the three diagonals contain the 12 letters of our honoree's name.
The White Rabbit 12-Puzzle,
2016
Butler University
The White Rabbit 12-Puzzle, Chris Morgan, Jeremiah Farrell
Scholarship and Professional Work - LAS
Martin Gardner's fondness for the characters and themes of Lewis Carroll's "Alice" is well-known and to honor Gardner we offer two word puzzles to be played on the 12-node diagram of the WHITE RABBIT.
