Applied Mathematics Commons^™

The Pi-Royal Tire, Erik Talvila

Journal of Humanistic Mathematics

In this humorous story, the half-wit proprietor of a tire manufacturing company thinks knowing pi to more digits will allow the production of rounder tires. An applied mathematician is recruited to fulfill a ridiculous industrial research agenda.

Waiting For The Magic: A Historical And Mathematical Study Of Queues In Disney Theme Parks, Nina E. Becket

Journal of Humanistic Mathematics

This paper, written as part of an honors research project in high school, provides an introduction to the line and queuing systems at Disney theme parks. We begin with a brief history of Disney World and its creators. We then introduce the basics of queuing theory and queuing notation. Finally, we examine modern line systems at Disney (as of 2023) and the future of its different queue systems.

A Method For Folding Origami Rectilinear Polygon Extrusions, Everett L. Jin

Journal of Humanistic Mathematics

We present a method for generating crease patterns for folding any rectilinear polygon extrusion with a specified uniform minimum edge-to-edge distance, using a rectangular sheet of paper. We demonstrate that the resulting models are efficient and watertight. In addition, they achieve optimal efficiency, meaning they attain the smallest possible scale factor from the original sheet of paper to the folded rectilinear polygon extrusion. Finally, we provide a code implementation of the method. Our study not only facilitates crease pattern design for origami artists but also offers an innovative, art-driven pedagogical tool for inspiring interest in mathematics.

Stylometric And Formal Patterns In The Scholarly Impact Of Scientific Literature, Joshua Ange, Eric Godat, Rajani Sudan

SMU Journal of Undergraduate Research

Scientific communication is typically tied to promoting public engagement and interest in science, increasing scientific literacy, and playing an essential role in policymaking. The success of public communication of scientific findings is largely associated with secondary characteristics of research (e.g. the style of writing and presentation), rather than the primary content or research quality. But it is unclear to what extent the success of scientific literature intended for working scientists is influenced by those same secondary characteristics. Does the writing style of scientific articles impact their success in academic spheres? In this study, we explore the stylometric and formal characteristics …

Fractsynth: Exploring Glitch Timbres With Chaos Theory, Aidan Roach

The Transdisciplinary STEAM+ Journal

In this paper, I explore how chaos theory can be used to design a new kind of synthesizer with the primary focus of producing glitchy, unpredictable sounds. Glitch music embraces abstract sound design, malfunctioning electronics, and randomness as the main compositional elements. However, most synthesizers rely on stable, repetitive oscillators that often sound too controlled. To challenge this, I developed FractSynth, a real-time synthesizer that uses chaotic attractors–including the Logistic Map, Henon Map, and Lorenz System–as modulation sources for frequency, amplitude, and tone. The software also features real-time Lyapunov Exponent Tracking, which gives users a direct visual of how …

Making Mathematical Art Via The Harmonic And Perturbed Harmonic Functions, Mehmet Pakdemirli

Journal of Humanistic Mathematics

Starting from the definition of a harmonic function series, we define a new series which we call the perturbed harmonic function series. We explore the relationship of the new series with the Weierstrass and Riemann fractal functions as well as its convergence and differentiability properties. We then illustrate the potential of the harmonic functions in generating complex figures that sometimes resemble natural objects, with explicit numerical examples.

Gold And Silver In Balance: Khayyam’S Mathematical Analysis Of Binary Alloys, Yousef Yassi, Reza Yassi

Journal of Humanistic Mathematics

The history of titration dates back to Archimedes who established that an object submerged in a liquid displaces an amount of liquid whose weight is equal to the buoyant force acting on the object. Since then, many scientists and engineers have tried to optimize his approach or devise new instruments for titration purposes. Omar Khayyam (1048–1123), in addition to designing a hydro-static balance, developed mathematical approaches for titration of binary alloys, that is, alloys made up of only two elements. Here we explore the different versions of Khayyam’s work on titration given by various sources. We also compare the accuracy …

Exploring The Dynamics Of Romantic Relationships Through The Lens Of Prem Rog, Umang Jain, Dheeraj Sharma, Pranay Goswami, Kuldeep Malik

Journal of Humanistic Mathematics

Romantic relationships are dynamic events that begin, grow, and frequently remain for a long time in a stagnant or fluctuating state until possibly dissipating. Although they are unquestionably the most significant dynamic events in our lives, dynamic systems theory has only recently included them in its formal framework. Without a mathematical model, it would be impossible to analyze and comprehend the dynamics because, in general, love stories are too brief to allow things to stabilize and are affected by the ups and downs of the surrounding community. In this paper, we set up models made up of four ordinary differential …

Modeling French Language Preservation: An Optimal Control Problem, Charlotte Blasi

Scripps Senior Theses

The French language is one of the most globally spoken languages, with over 300 million speakers and designated the official language of 29 nations. French continues to prosper as a result of its titular nations' imperialist history that emphasized linguistic diffusion as well as the support of international organizations dedicated to promoting both the language and the culture of French-speaking nations. In this thesis, we explore the nuanced history of French-speaking countries and one institution dedicated  to promoting the French language, the OIF. We further examine the media mechanism of the OIF and construct a system of Ordinary Differential Equations …

Invitation To Polynomiography Via Chatgpt: For Teachers, Students And Artists, Bahman Kalantari

LASER Journal

Teachers, students, and artists in the United States and abroad who have encountered polynomiography, in lectures, demos, or software, consistently appreciate its educational value and artistic potential. While dedicated polynomiography programs require upkeep as systems evolve, AI chatbots now offer a practical, accessible alternative. This article invites readers to explore polynomiography with ChatGPT, broadening access beyond specialized tools. While the approach will not match the full range or polish of advanced software, it provides a powerful and flexible entry point with many possibilities.

At its core, polynomiography transforms polynomial equations, each encoding a finite set of points in the complex …

Modifications To The Spiral Array: A Computational Approach To Music Analysis, Rose Bittle

DePaul Discoveries

The Spiral Array is a geometric model of musical tonality and exists as a tool in computer-aided music analysis. The model was first published in 2000 by Elaine Chew, PhD, in her thesis, Towards a Mathematical Model of Tonality. This project aimed to restructure the Spiral Array, limiting user ambiguity and optimizing the application of musical key finding. The existing model defines pitch, chord, and key location to form a series of spirals dependent on a set of flexible weights. In our research we were able to identify potential issues with the pitch definitions themselves and experiment with methods …

The Other Side Of The Equation: De-Simplification, A Prerequisite For Calculus, Stephen L. Brown

ACMS Conference Proceedings 2005

No abstract provided.

Suntan (And Other Solar Trigonometric Functions): Solutions For Fermi Questions: February 2025, John Adam

Mathematics & Statistics Faculty Publications

The article discusses the intensity of sunlight on the side of the author's face as they walk to and from their office, focusing on the solar zenith angle θ. It presents a formula for solar irradiance and explores how the intensity changes based on the angle and elevation. The solutions to the questions posed in the article provide insights into the maximum irradiance levels at different angles and elevations.

Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck

Scripps Senior Theses

How might we bring an idea to life from both a mathematical and an artistic perspective? Within Weathering, I use imagery of environmental erosion to explore the differences between physical and digital forms of representation. I created a physical painting of an abandoned copper mine, digitized the work, and then used a mathematical model to digitally “erode” it, which I re-translated into paintings. While the explicit texture present in physical work speaks best to my practice/intent, the mathematical framework that is the basis for my digital work affords a powerful mode of temporal flexibility. Used in conjunction, these two …

Ultrasonic Sensor-Based Sound Synthesis Using Raspberry Pi Pico W, Niraj Jaishwal

Williams Honors College, Honors Research Projects

At the intersection of Human Computer Interaction and digital art, this project transforms simple motion into musical expression. It explores an interactive real-time sound synthesis system using ultrasonic sensors to generate continuous audio. The objective is to design a system that maps physical distances into musical parameters such as pitch and amplitude, which will create a responsive audio environment. Two ultrasonic sensors are used in combination with the Raspberry Pi Pico W microcontroller running CircuitPython and Adafruit Audio Hat for real-time sound output. One sensor controls the pitch of the generated tone, while the other controls volume. This enables expressive …

Learning Paradigms For Rhythm Detection And Generation Using Mathematical Models, Biophysical And Artificial Neural Networks, Prianka Bose

Dissertations

Humans possess an inherent ability to recognize evenly-spaced rhythms, known as isochronous rhythms, owing to the brain's predisposition to entrain to external auditory stimuli with regular temporal intervals. The central focus of this research is to understand how the brain learns and retains rhythmic time intervals in the context of music. This dissertation studies rhythm detection and generation through mathematical models, biophysical networks, and artificial neural networks, addressing both isochronous and non-isochronous patterns.

A primary focus of the thesis is on isochronous rhythms. In particular, given a perturbation to an isochronous rhythm such as a tempo change or phase shift …

The History Of The Billboard Hot 100 And Its Process, Brileigh Cates

Undergraduate Research Conference at Missouri S&T

The Billboard Hot 100 has been around for decades, and it is believed without much accreditation. What really is Billboard, and why is it so popular? Why have other charting companies not taken up as much popularity? How does Billboard determine the popularity of artists? How has this changed with the introduction of the internet? This research project addresses all of these question, allowing the validity of the data collection to be addressed.

Gender And The Billboard Top 40 Charts Between 1958 And 2023, Brileigh Cates, Justin W. Pope

Undergraduate Research Conference at Missouri S&T

Is there an inherent bias towards male artists in the music industry? Evidence has been shown in previous studies, the most recent being from 2017, that there may be bias towards male artists appearing in Billboard Magazine s Hot 100 list. This study not only updates previous data to include 2017 through 2023, but also looks at the top 40 charts on a week-by-week bias as opposed to the year-end charts that other studies used for their data. We coded each song so as to indicate the gender of the artist(s) as well as whether or not the artists appeared …

Casar Public Lecture: "Women & Stem Education In Egypt & The Us: Stepping Into A Man's World Of Science & Technology", The Prince Alwaleed Center For American Studies And Research Casar, Yasmeen El Ghazaly, Mark W. Deets

Performances, Events, and Presentations

In celebration of International Women's Day this Month, we held a public lecture titled: "Women & STEM Education in Egypt & the US : Stepping into a Man's World of Science & Technology " on Thursday March 28th, 2024 from 12:15 pm to 1:15 pm (assembly hour) – Conference and Visitor Center, Mary Cross Hall AUC New Cairo Despite a plethora of advances made by women in the world we live in today, they are still woefully underrepresented in the realm of STEM education and the associated career paths. At this event, we uncovered the history, reasons & challenges women …

Inhabiting Numbers: Weaving, Polyphony, And Embodied Mathematics, Kristine Barrett

Textile Society of America: Symposium Proceedings

Inhabiting Numbers: Polyphony as Woven Sound explores connections between vocal polyphony and textile practices, specifically weaving and spinning. Rather than consider music and weaving as separate from one another, the following paper presents the ways in which they are deeply intertwined and mutually constitutive forms of cultural expression. The technical modes of thinking produced through repetition inherent in both—particularly as practices utilizing complex mathematical structures—produce ways of thinking unique to each. Through practice, I suggest these technical modes of making transit across different materials and mediums—in both explicit and implicit ways. The music created through the interweaving of multiple voices …

The Convergence Of Ikigai And Design Thinking: Crafting A Purposeful Framework, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In an era where innovation is not just about solving problems but also about enhancing human experiences and fostering personal fulfillment, the convergence of Ikigai principles with Design Thinking methodology offers a promising avenue for holistic problem-solving and in-novation. This paper explores the intersection of Ikigai—a Japanese concept representing one's reason for being—and Design Thinking—a human-centered approach to innovation. We propose a conceptual framework, termed Ikigai-Driven Design (IDD), which integrates the principles of Ikigai with the stages of Design Thinking. IDD comprises five main stages: Empathize, Define, Ideate, Prototype, and Test, each combining elements of Ikigai and Design Thinking to …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Balanced Blended Space: Proposing A Universal Theoretical Framework For Combinative Reality, David Smith, Frederick Bianchi

Publications and Research

In today's fragmented societies, a unified framework for communication and collaboration across different realities is crucial. We introduce Balanced Blended Space (BBS) as a framework for describing combinative reality, encompassing virtual, physical, and conceptual realms, all intrinsically connected. Interactions within these environments shape our perceptual space. This paper outlines key axiomatic assumptions, criteria for a universal framework, and fundamental terminology. We identify deep symmetries enabling the BBS framework, including Cognitive and Computational Symmetry, Physical and Virtual Symmetry, Mediation Pathway Symmetry, Space-Time Symmetry, and Sensory Symmetry. We propose tests to determine its viability, emphasizing virtual intelligence as a collaborative partner. We …

Proposing A Measure Of Ethicality For Humans And Ai, Alejandro Jorge Napolitano Jawerbaum

Electronic Theses and Dissertations

Smarter people or intelligent machines are able to make more accurate inferences about their environment and other agents more efficiently than less intelligent agents. Formally: ‘Intelligence measures an agent’s ability to achieve goals in a wide range of environments.’ (Legg, 2008)

In this dissertation we extend this definition to include ethical behaviour and we will offer a mathematical formalism and a way to estimate how ethical an action is or will be, both for a human and for a computer, by calculating the expected values of random variables. Formally, we propose the following measure of ethicality, which is computable, or …

Du Undergraduate Showcase: Research, Scholarship, And Creative Works, Caitlyn Aldersea, Justin Bravo, Sam Allen, Anna Block, Connor Block, Emma Buechler, Maria De Los Angeles Bustillos, Arianna Carlson, William Christensen, Olivia Kachulis, Noah Craver, Kate Dillon, Muskan Fatima, Angel Fernandes, Emma Finch, Colleen Cassidy, Amy Fishman, Andrea Francis, Stacia Fritz, Simran Gill, Emma Gries, Rylie Hansen, Shannon Powers, Jacqueline Martinez, Zachary Harker, Ashley Hasty, Mykaela Tanino-Springsteen, Kathleen Hopps, Adelaide Kerenick, Colin Kleckner, Ci Koehring, Elijah Kruger, Braden Krumholz, Maddie Leake, Lyneé Alves, Seraphina Loukas, Yatzari Lozano Vazquez, Haley Maki, Emily Martinez, Sierra Mckinney, Audrey Mitchell, Kipling Newman, Audrey Ng, Megan Lucyshyn, Andrew Nguyen, Stevie Ostman, Casandra Pearson, Alexandra Penney, Julia Gielczynski, Tyler Ball, Anna Rini, Christina Rorres, Simon Ruland, Helayna Schafer, Emma Sellers, Sarah Schuller, Claire Shaver, Kevin Summers, Isabella Shaw, Madison Sinar, Claudia Pena, Apshara Siwakoti, Carter Sorensen, Madi Sousa, Anna Sparling, Alexandra Revier, Brandon Thierry, Dylan Tyree, Maggie Williams, Lauren Wols

DU Undergraduate Research Journal Archive

DU Undergraduate Showcase: Research, Scholarship, and Creative Works

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

Poster Session, Emma Beeler, Maddison Caldwell, Mackenzie Paul, Shirli Salihaj, Sara Lynn Sligh, Stephen Trest

Mississippi Undergraduate Honors Conference

Video provided is of MacKenzie Paul's presentation.

Abstracts

Humanities

Emma Beeler, Mississippi University for Women

Adultery and Fidelity in the Lais of Marie de France

Using both literary and historical analysis, I will examine contrasting depictions of adultery and fidelity within the lais written by 12th-century poet Marie de France. A lai is a type of narrative poem, ranging in length from 118 to 1184 lines. Many of Marie de France’s lais follow the literary trope known as courtly love; however, the reader is encouraged to sympathize with different characters depending on the lai. In some lais, the reader …

The World As We Know It: Maps And Atlases From Special Collections, Archives And Special Collections, Luke Meagher

Library Exhibits

Selections of maps and atlases from Sandor Teszler Library’s Special Collections are presented in this exhibit to show how, over time, cartographers have represented the world as we know it.