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Mathematics

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Full-Text Articles in Art and Design

Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo Mar 2019

Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo

The STEAM Journal

The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of ...


Unfolding Humanity: Cross-Disciplinary Sculpture Design, Gordon D. Hoople, Nate Parde, Quinn Pratt, Sydney Platt, Michael Sween, Ava Bellizzi, Viktoriya Alekseyeva, Alex Splide, Nicholas Cardoza, Christiana Salvosa, Eduardo Ortega, Elizabeth Sampson Mar 2019

Unfolding Humanity: Cross-Disciplinary Sculpture Design, Gordon D. Hoople, Nate Parde, Quinn Pratt, Sydney Platt, Michael Sween, Ava Bellizzi, Viktoriya Alekseyeva, Alex Splide, Nicholas Cardoza, Christiana Salvosa, Eduardo Ortega, Elizabeth Sampson

The STEAM Journal

Unfolding Humanity is a 12 foot tall, 30 foot wide, 2 ton interactive metal sculpture that calls attention to the tension between technology and humanity. This sculpture was conceived, designed, and built by a large group (80+) of faculty, students, and community volunteers at the University of San Diego (USD). The piece is a dodecahedron whose pentagonal walls unfold under human power, an engineered design that alludes to Albrecht Dürer's 500-year-old unsolved math problem on unfolding polyhedra. When closed, the mirrored interior of the sculpture makes visitors feel as though they are at the center of the universe. The ...


Volume 11, Jacob Carney, Ryan White, Joseph Hyman, Jenny Raven, Megan Garrett, Ibrahim Kante, Summer Meinhard, Lauren Johnson, William "Editha" Dean Howells, Laura Gottschalk, Christopher Siefke, Pink Powell, Natasha Woodmancy, Katharine Colley, Abbey Mays, Charlotte Potts Jan 2019

Volume 11, Jacob Carney, Ryan White, Joseph Hyman, Jenny Raven, Megan Garrett, Ibrahim Kante, Summer Meinhard, Lauren Johnson, William "Editha" Dean Howells, Laura Gottschalk, Christopher Siefke, Pink Powell, Natasha Woodmancy, Katharine Colley, Abbey Mays, Charlotte Potts

Incite: The Journal of Undergraduate Scholarship

Table of Contents:

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Synthesis of 3,5-substituted Parabens and their Antimicrobial Properties, Jacob Coarney, Ryan White

Chernobyl: Putting "Perestroika" and "Glasnot" to the Test, Joseph Hyman

Art by Jenny Raven

Watering Down Accessibility: The Issue with Public Access to Alaska's Federal Waterways, Meagan Garrett

Why Has the Democratic Republic of the Congo outsourced its Responsibility to Educate its Citizens? Ibrahim Kante

Art by Summer Meinhard

A Computational Study of Single Molecule Diodes, Lauren Johnson

Satire of the State through ...


Stranded Cellular Automaton And Weaving Products, Hao Yang Sep 2018

Stranded Cellular Automaton And Weaving Products, Hao Yang

Mathematical Sciences Technical Reports (MSTR)

In order to analyze weaving products mathematically and find out valid weaving products, it is natural to relate them to Cellular Automaton. They are both generated based on specific rules and some initial conditions. Holden and Holden have created a Stranded Cellular Automaton that can represent common weaving and braiding products. Based on their previous findings, we were able to construct a Java program and analyze various aspects of the automaton they created. This paper will discuss the complexity of the Stranded Cellular Automaton, how to determine whether a weaving product holds together or not based on the automaton and ...


Rediscovering The Interpersonal: Models Of Networked Communication In New Media Performance, Alicia Champlin Aug 2018

Rediscovering The Interpersonal: Models Of Networked Communication In New Media Performance, Alicia Champlin

Electronic Theses and Dissertations

This paper examines the themes of human perception and participation within the contemporary paradigm and relates the hallmarks of the major paradigm shift which occurred in the mid-20th century from a structural view of the world to a systems view. In this context, the author’s creative practice is described, outlining a methodology for working with the communication networks and interpersonal feedback loops that help to define our relationships to each other and to media since that paradigm shift. This research is framed within a larger field of inquiry into the impact of contemporary New Media Art as we experience ...


Using Three Fields Of Education Research To Frame The Development Of Digital Games, Michelle Zandieh, David Plaxco, Caro Williams-Peirce, Ashish Amresh Jun 2018

Using Three Fields Of Education Research To Frame The Development Of Digital Games, Michelle Zandieh, David Plaxco, Caro Williams-Peirce, Ashish Amresh

Ashish Amresh

No abstract provided.


Rudolf Laban's Dream: Re-Envisioning And Re-Scoring Ballet, Choreutics, And Simple Functional Movements With Vector Signs For Deflecting Diagonal Inclinations, Jeffrey Scott Longstaff Jun 2018

Rudolf Laban's Dream: Re-Envisioning And Re-Scoring Ballet, Choreutics, And Simple Functional Movements With Vector Signs For Deflecting Diagonal Inclinations, Jeffrey Scott Longstaff

Journal of Movement Arts Literacy

Several methods of movement notation, forerunners of modern-day Labanotation/Kinetography were published by Rudolf Laban in his 1926 book Choreographie. One of these has been referred to as vector signs because they represent movement as orientations (slopes) of lines through space. This article begins by comparing Labanotation direction symbols with Laban's earlier vector signs by looking at differences when simple sequences are scored in both formats. Concepts of space within the vector signs are examined, particularly Laban's idea of deflecting inclinations where movements are categorized as mixtures of two fundamental contrasting spatial and dynamic tendencies: dimensional stability and ...


Geometric Serendipity, Dakota Becker Jan 2018

Geometric Serendipity, Dakota Becker

Auctus: The Journal of Undergraduate Research and Creative Scholarship

The central focus of my practice is the serendipitous exploration into geometry, symmetry, design, and color. I have found more and more that the affinity I have for hard-edge geometric abstraction is a deeper reflection of the way in which I process my thoughts and surroundings. In the past year, I have sought to challenge myself by questioning the core of my practice and pushing it to go beyond its individual elements. In this way, I seek to create work that is more than its parts. As a result, I have become more purposeful with my designs and push both ...


What's Cooler Than Being Cool? Ice-Sheet Models Using A Fluidity-Based Fosls Approach To Nonlinear-Stokes Flow., Jeffery M. Allen Jan 2017

What's Cooler Than Being Cool? Ice-Sheet Models Using A Fluidity-Based Fosls Approach To Nonlinear-Stokes Flow., Jeffery M. Allen

Applied Mathematics Graduate Theses & Dissertations

This research involves a few First-Order System Least Squares (FOSLS) formulations of a nonlinear-Stokes flow model for ice sheets. In Glen's flow law, a commonly used constitutive equation for ice rheology, the viscosity becomes infinite as the velocity gradients approach zero. This typically occurs near the ice surface or where there is basal sliding. The computational difficulties associated with the infinite viscosity are often overcome by an arbitrary modification of Glen's law that bounds the maximum viscosity. The FOSLS formulations developed in this thesis are designed to overcome this difficulty.

The first FOSLS formulation is just the first-order ...


Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus May 2016

Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus

Celebration of Student Scholarship Posters Archive

No abstract provided.


Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams May 2016

Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams

Celebration of Student Scholarship Posters Archive

No abstract provided.


A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look Jul 2015

A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look

Journal of Humanistic Mathematics

The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.


What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin Jun 2015

What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin

Publications and Research

For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence ...


Using Maya And Mathematica To Create Mathematical Art, Allison Carr May 2015

Using Maya And Mathematica To Create Mathematical Art, Allison Carr

Honors Projects

The project consists of six pieces of art that were created in Maya using mathematical objects created in Mathematica. Accompanying the art are artist statements for each piece, the mathematics behind each object used, and the Mathematica codes used to generate the objects.


Geometry: Drawing From The Islamic Tradition, Carol Bier Jan 2015

Geometry: Drawing From The Islamic Tradition, Carol Bier

Carol Bier

Getting students involved in careful observation and analysis and encouraging their exploration of cultural forms of expression is an excellent means of introducing mathematical ideas. Geometric patterns abound in Islamic art and architecture. Exhibiting great ingenuity over the centuries, Muslim artists and craftsmen created beautiful patterns to adorn architectural monuments and exquisite objects. The Alhambra in Spain and the Taj Mahal in India offer the most famous examples of extraordinary patterns using brick and glazed tile, or carved and inlaid marble. Other examples of patterns are made using metal, wood, and fiber. Students may gain conceptual and theoretical understanding of ...


Drawing Numbers And Listening To Patterns, Loren Zo Haynes Jan 2015

Drawing Numbers And Listening To Patterns, Loren Zo Haynes

University Honors Program 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 ...


Morphological Operations Applied To Digital Art Restoration, M. Kirbie Dramdahl Aug 2014

Morphological Operations Applied To Digital Art Restoration, M. Kirbie Dramdahl

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

This paper provides an overview of the processes involved in detecting and removing cracks from digitized works of art. Specific attention is given to the crack detection phase as completed through the use of morphological operations. Mathematical morphology is an area of set theory applicable to image processing, and therefore lends itself effectively to the digital art restoration process.


Session B-1: Geometry In Art & Architecture, Julie Dowling Feb 2014

Session B-1: Geometry In Art & Architecture, Julie Dowling

Professional Learning Day

Math is all around us! Discover how to implement geometry lessons using art and architecture that the students see around them every day.


The Math - Craft Connection, Julie Killian May 2013

The Math - Craft Connection, Julie Killian

Honors Projects and Presentations: Undergraduate

The connection between mathematics and art is ancient. In times long ago, scholars did not divide the two subjects as arbitrarily as many do today. In fact, according to Morris Kline, “geometry, philosophy, logic, and art were all expressions of one type of mind, one outlook on the universe” [10]. The Greeks, for instance, considered mathematics to be an art based on its qualities of order, consistency, completeness, and definiteness, which to them defined beauty. In the eighteenth century, scholars tried to define beauty by mathematical formulas, unfortunately without great success. Kline also makes a 20th-century argument for ...


How Mathematics Influences Our Perception Of Beauty, Leslie Muzulu Apr 2013

How Mathematics Influences Our Perception Of Beauty, Leslie Muzulu

Antonian Scholars Honors Program

Beauty is an important part of our lives. Consequently, it is no surprise that we are interested in our experiences and judgments of it. What makes something beautiful? The arts and nature are considered vessels of beauty, but could mathematics be as well? Can it influence our perception of what is beautiful? This paper offers insights into how mathematics influences our perception of what is beautiful. The philosophies of aesthetics and mathematics are briefly discussed, followed by a consideration of how the presence of such mathematical structures as proportion, symmetry and perspective can significantly influence our perception of beauty in ...


Propeller, Joel Kahn Mar 2013

Propeller, Joel Kahn

The STEAM Journal

This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.


Methods In Visual Mathematics: Reductionism In Researching Mathematical Principles In Art, Lauren N. Colie Jan 2013

Methods In Visual Mathematics: Reductionism In Researching Mathematical Principles In Art, Lauren N. Colie

Auctus: The Journal of Undergraduate Research and Creative Scholarship

People traditionally rely on visual arts as an effective communication tool and medium of self-expression for when words fail to convey abstract concepts. Thera Mjaaland, anthropologist and professional photographer, writes, “Art is capable of negotiating conceptual gaps caused by a dichotomized epistemology” (393). In essence, Mjaaland asserts that art helps relate different modes of thinking by illustrating the abstract and difficult to grasp—privileging the communicative value of an image over that of text. Within this method of communication is a collection of works acknowledged by public consensus to be of an elevated status or value. The art world is ...


Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii", Heidi Burgiel, Matthew Salomone Jan 2012

Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii", Heidi Burgiel, Matthew Salomone

Journal of Humanistic Mathematics

M.C. Escher's use of dilation symmetry in Path of Life III gives rise to a pattern of logarithmic spirals and an oddly ambiguous sense of depth.


A Linear Perspective To Art, Sarah Littler Jan 2004

A Linear Perspective To Art, Sarah Littler

Humanistic Mathematics Network Journal

No abstract provided.


Loopy, George W. Hart Jun 2002

Loopy, George W. Hart

Humanistic Mathematics Network Journal

No abstract provided.


Mathematical Aspects Of Oriental Carpets, Carol Bier Jan 2001

Mathematical Aspects Of Oriental Carpets, Carol Bier

Carol Bier

The mathematical principles of pattern making according to symmetrical repetition are well-known today, but the mathematical aspects of pattern formation have been glossed over in the study of Oriental carpets, or neglected in favor of either an appreciation of color and form or a discussion of social and ethnic origins. This article seeks to address several mathematical aspects of Oriental carpets, which are both integral to their form and manifest in their visual make-up.


Art And Geometry: Proportion And Similarity, Catherine A. Gorini Jul 1999

Art And Geometry: Proportion And Similarity, Catherine A. Gorini

Humanistic Mathematics Network Journal

No abstract provided.


Spirograph® Math, Karin M. Deck Mar 1999

Spirograph® Math, Karin M. Deck

Humanistic Mathematics Network Journal

No abstract provided.


Illumination And Geometry In Islamic Art, Salma Marani Jul 1997

Illumination And Geometry In Islamic Art, Salma Marani

Humanistic Mathematics Network Journal

No abstract provided.


See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine Jul 1997

See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine

Humanistic Mathematics Network Journal

No abstract provided.