Physical Sciences and Mathematics Commons^™

Creating Art With The Generalized Pythagorean Theorem, Ángel Colín

Journal of Humanistic Mathematics

The Pythagorean Theorem and its generalizations have been widely studied. In this article we focus on one particular generalization that asserts that the area of a polygon with one side the hypotenuse of a right triangle is the sum of the areas of similar polygons whose corresponding sides are the other two sides [4]. Using this theorem together with interactive software or simply pencil and paper, we create some visually enticing artwork. This activity, we believe, can contribute positively to geometry teaching at all academic levels.

Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca

Journal of Humanistic Mathematics

We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …

Partnering With Students To Create A Positive Image Of Mathematics, Manmohan Kaur

Journal of Humanistic Mathematics

In a 1989 paper, Barbeau states, “Probably no area of human activity is as afflicted as mathematics with a gap between the public perception of its nature and what its practitioners believe it to be.” Decades later, the situation is much the same. With the technical advances in the contemporary world, mathematics affects our day-to-day activities in essential ways such as e-commerce and credit card security. Mathematical problem solving intrinsically requires creative and critical thinking. However, mathematics is often perceived as uninventive, sterile, static, and removed from human needs and culture. This paper describes how mathematicians can own the image …

Why Read The Classics (Of Mathematical Proofs)?, Cosimo Perini Brogi

Journal of Humanistic Mathematics

Inspired by Italo Calvino’s (almost) homonymous writing, this short essay suggests a formal perspective to complement the typical categorisation of classical results in mathematics on aesthetic bases. The traditional proof that √2 is not a rational number provides a simple example of proof mining. When studied through the tools of logic, that proof has also led to designing new systems for formal proving based on cyclic proofs. This example thus supports the central thesis of this essay that reading the classics of mathematical proofs enables us to acquire a taste for mathematical beauty and can open new directions in mathematics …

A Mathematician Expresses Grief, Richard Delaware

Journal of Humanistic Mathematics

A famous Scottish mathematician of the eighteenth century shares a tragic sorrow.

How (And Why) To Start A Math Circle At The County Jail, Aram Bingham

Journal of Humanistic Mathematics

Math circles are a common form of outreach usually run by professional mathematicians as enrichment for K-12 students or teachers. As a setting to stimulate interest and develop positive socialization around mathematical practice, a regular math circle can also be an effective bridge to higher education in carceral settings for both facilitators and participants. This article describes my journey through starting and running math circles in county jails, with a view towards the expansion of mathematics education as another tool for the dismantling of mass incarceration.

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.

A Note On Modeling Prejudice, Alan Lockard, Edwin Harcourt

Journal of Humanistic Mathematics

We model prejudice in the context of an iterated prisoner’s dilemma tournament. Prejudice here is defined as the inability to distinguish amongst members of an identifiable group. We run a computer simulation where agents of one of two groups with defined strategies are randomly matched against each other. The agents either cooperate with or defect against the agent they are matched with. Our focus is on agents who play an unprejudiced version of the Tit-for-Tat strategy (cooperate with any player in the first encounter, and then apply the same strategy [defect or cooperate] that the opposing player played against them …

How Did Cauchy Prove His Integral Theorem? A Historical Reconstruction For Education Research, José Gerardo Piña-Aguirre, Rosa María Farfán Márquez

Journal of Humanistic Mathematics

In his article “Mémoire sur les Intégrales Définies, prises entre des limites imaginaires” of 1825, Cauchy proves that the integral of a complex function f defined on complex numbers is independent of the path of integration if the function f remains finite and continuous along the chosen path. In contemporary literature that analyzes the mathematics of Cauchy, the specific mathematical process that allowed Cauchy to prove this result is not explicitly presented. The purpose of this manuscript is to communicate a symbolic-algebraic derivation that justifies the narrative argument used by Cauchy to support his proof, thus hopefully filling this gap. …

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 …

A Just Balance And The Teaching And Learning Of Mathematics, Marshall Gordon

Journal of Humanistic Mathematics

Society’s response to the question of what is worth sharing and how it best can be provided as conceived by the educational establishment shapes the education of every individual in school. As the classroom experience is a commitment to the future of society, it is good and just for society to support the educational development of each person in order that all can participate productively. In this way a “just balance” is established. In the particular case of educating students in mathematics, however, there is apparently an unjust balance, for despite the considerable time and effort students and teachers in …

Polygonal Number Similarity, Gunhan Caglayan

Journal of Humanistic Mathematics

This note takes an exploratory approach to define and then visualize the notion of polygonal number similarity between pairs of k-gonal numbers P_k(αn) and P_k(n) , where α is an integer scale factor of 2 or greater.

Translating Trattato Dell'alcibra Amuchabile, Olympia Nicodemi

Journal of Humanistic Mathematics

We present a detailed look at one small section of a premodern algebra manuscript from circa 1365 C.E. The manuscript, Tratatto dell’Alcibra Amuchabile (Anonimo), is written in the Tuscan vernacular, with no symbols, no punctuation, and wildly inconsistent (pre-printing press) spellings. We present some of the hurdles to translating this “rhetorical algebra” followed by an annotated translation of one of its algebra rules, Rule 5, through which we learn the methods and mindset of algebra that preceded and seeded the breakthroughs in algebra of the 16^th century. We also point to some of the significant differences between algebra then …

Mathematics And Ethics: Narratives And Conversations, David Pritchard

Journal of Humanistic Mathematics

We provide an eclectic overview of various narratives that mathematicians use to describe mathematics. We discuss some of the ethical issues and approaches that each narrative tends to emphasise, and how these can lead to productive conversation in the absence of a universally agreed philosophical or ethical framework. We also discuss the dangers of a deficit model of ethical engagement, and other threats to conversation.

A Schur-Fire Way To Make Matrix Products Coincide, Keith Copenhaver, Josh Hiller, Christopher Sciortino

Journal of Humanistic Mathematics

When are the Schur product and the matrix product of two matrices the same? With the help of Morpheus (from The Matrix) and more, we explore this question and find both mathematical answers and math-memes.

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 …

The More Things Change..., Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Microplastics In St. John, United States Virgin Islands Sediments: Methodological Approaches And Variability Of Microplastics Concentrations And Accumulation Rates, Henry B. Arbaugh, Sarah C. Gray, Dimitri Deheyn

Theses

Sediment samples were collected from a near shore and reef site in Coral Bay, St. John, United States Virgin Islands (USVI) from 2007-2016, using tube sediment traps. These samples provide an opportunity to study microplastics (MPs) in an area where no previous MP studies have been performed. Most sedimentary MP studies utilize benthic samples which can only measure MP concentrations (#MP/g or #MP/mL sediment), while sediment traps can provide MP accumulation rates (#MP/cm²/day) as a function of time. However, the methods used for extracting MPs from benthic samples have not been tested using sediment trap samples whose characteristics, …

Estimasi Proporsi Pekerja Anak Pulau Maluku & Papua: Pendekatan Small Area Estimation Hierarchical Bayes Distribusi Beta, Apriani Sofiana, Fauzana Afininnas, Fachrol Mochti, Angga Prayoga, Shafira Husna, Nofita Istiana

Jurnal Ekonomi Kependudukan dan Keluarga

Pekerja anak merupakan isu krusial yang memerlukan penanganan segera untuk mendukung pencapaian target pembangunan global. Pengentasan isu ini menuntut ketersediaan data yang akurat hingga wilayah kecil guna mendukung perumusan kebijakan yang tepat sasaran. Penelitian ini bertujuan menduga proporsi pekerja anak usia 5–17 tahun di kabupaten/kota Pulau Maluku dan Papua tahun 2024 menggunakan metode Small Area Estimation (SAE) Hierarchical Bayes (HB) distribusi Beta. Lima variabel penyerta dari PODES dan regsosek dipilih melalui stepwise regression dan dieksplorasi secara spasial. Hasil pemodelan HB Beta Pulau Maluku dan Papua menunjukkan sebagian besar wilayah masih memiliki RSE tinggi. Untuk meningkatkan presisi, dilakukan klasterisasi wilayah sebelum …

Evaluation Of Large Language Models As Decision Support Tools For Head And Neck Cancer Management: A Blinded Multidisciplinary Simulation Study, Sholem Hack, Ron J. Karni, Antonino Maniaci, Christopher E. Fundakowski, Luca Castellani, Fabiola Incandela, Remo Accorona, Miguel Mayo-Yanez, Martina Violati, Lorenzo Giannini, Niccolo' Mevio, Alberto Maria Saibene

Department of Otolaryngology - Head and Neck Surgery Faculty Papers

BACKGROUND: The management of head and neck cancer relies on multidisciplinary expertise; however, access to tumor boards remains variable. Large language models (LLMs) may support guideline-based decision-making, although performance in complex oncologic scenarios is not well defined.

METHODS: Fourteen synthetic cases based on real tumor board encounters were evaluated. Five blinded comparator arms produced recommendations: a human expert, Non-RAG-GPT-4, Non-RAG-GPT-5, RAG-GPT-4, and RAG-GPT-5. Eight head and neck oncologic surgeons scored each recommendation for appropriateness, clarity, specificity, and feasibility using 5-point Likert scales. Paired permutation testing and inter-rater reliability were assessed.

RESULTS: LLM outputs showed close alignment with expert recommendations. RAG-based …

Reachability In Interactive Chemical Reaction Networks, Aberto Avila-Jimenez, Bin Fu, Elise Grizzell, Robert Schweller, Tim Wylie

Computer Science Faculty Publications

This paper studies the effects of interactivity on molecular computation, specifically in the Step Chemical Reaction Networks model (Step CRNs), by adding the ability for a user to interact with the system by selecting which species to add at each step, or by having some control over which reactions execute. The two proposed variants are Interactive CRNs and Randomized Interactive CRNs. We show that in Interactive CRNs, even when restricted to void (deletion-only) rules of relatively small size, if a user can decide which species to add at each step based on the configuration, reachability is PSPACE-complete when bounded and …

The Ai Academic Integrity Dichotomy: A Gender Lens, N. Sayegh, S. Larloulian, A. C. Elias, Leila Halawi

Publications

Using a gender lens, this research explores the intersection of artificial intelligence (AI) educational tools and academic integrity. Studies suggest gender differences exist in academic dishonesty rationalization, with males potentially exhibiting more opportunistic behaviors. This qualitative study collected data through 30-minute face-to-face semi-structured interviews, recorded with consent, and analyzed thematically. Four significant themes emerged: Gender Perspectives on AI Tool Usage, Patterns of AI Tool Utilization, Academic Integrity Concerns, and Implications of Academic Dishonesty. The results indicate that educational establishments should adopt responsible AI governance frameworks and ethical guidelines to uphold academic standards while promoting scholarly integrity and institutional trust.

Electronic Transport In Twisted Bilayer Tungsten Diselenides, Walid Zaher

Theses and Dissertations

This thesis investigates density waves (DWs) in twisted bilayer tungsten diselenide (tWSe₂) using a mean field approximation, with a focus on electron-electron interactions, and the system’s free energy at zero temperature. For the mean field approximation, the study initially employed same-spin nesting vectors, which were found insufficient to induce DWs formation. In contrast, when opposite-spin nesting vectors were used, DWs emerged, indicating that these vectors can support DWs formation. The plots were produced under perfect nesting conditions, where van Hove singularities (VHS) occur. At zero temperature, perfect nesting provides a complete picture of the upper limit of DWs formation, as …

A Virtual-Reality-Based Dental Simulator For Endodontics With Automated Formative Feedback, Yousef Salah Abo El Ela

Theses and Dissertations

Advancements in virtual reality (VR) and haptic technology are transforming the landscape of medical and dental education, offering new avenues for safe, immersive, and repeatable training experiences. Within dentistry, endodontics presents unique challenges for preclinical education due to anatomical complexity, limited access to extracted teeth, ethical concerns, and the shortcomings of conventional plastic models. Despite endodontics specific plastic teeth being available, they fall short of replicating the hardness of real extracted teeth, are relatively costly compared to generic plastic teeth, and are ultimately a disposable item which makes them inadequate as a sustainable long-term solution. Extracted teeth do a much …

A Computational Study Of The Chemomechanics Of Paracetamol Polymorphs: Towards Improving Drug Tabletability, Karim Nader Samra

Theses and Dissertations

The mechanical properties of pharmaceutical crystals are of great importance in tablet manufacturing. Also, knowing the mechanical properties of different polymorphs of the same crystal can reduce the overall production cost. In this study, computational work was done via performing density functional theory calculations on 3 paracetamol crystal polymorphs Form I, II, and III. Understanding the chemical bonding helps in predicting the key elastic properties for different crystallographic directions. In Form II, lattice vector C is dominated with the intermolecular hydrogen bond OH…O giving it the stiffest Young Modulus and the least Poisson’s ratio. Then comes the A-Axis which contains …

Potent, Selective Pyrrolopyrimidine Pde11a4 Inhibitors With Improved Pharmaceutical Properties, Shams Ul Mahmood, Rama Krishna Boddu, Jeremy Eberhard, Charles S. Hoffman, John Gordon, Dennis Colussi, Wayne Childers, Elvis Amurrio, Marie Danaher, Michy P. Kelly, David P. Rotella

Department of Chemistry and Biochemistry Faculty Scholarship and Creative Works

Previous work demonstrated target engagement with an orally bioavailable, potent, selective PDE11A4 inhibitor in the mouse hypothalamus. This compound was limited by low aqueous solubility, stimulating the need for alternative leads with improved pharmaceutical properties to carry out efficacy studies. This paper outlines optimization of a pyrrolopyrimidine hit leading to a potent, selective PDE11A4 inhibitor with improved pharmaceutical properties and promising activity in cell-based models of enzyme activity.

Quantum Benchmarking Of High-Fidelity Noise-Biased Operations On A Detuned Kerr-Cat Qubit, Bingcheng Qing, Ahmed Hajr, Ke Wang, Gerwin Koolstra, Long B. Nguyen, Jordan Hines, Irwin Huang, Bibek Bhandari, Larry Chen, Ziqi Kang, Christian Jünger, Noah Goss, Nikitha Jain, Hyunseong Kim, Kan-Heng Lee, Akel Hashim, Nicholas E. Frattini, Zahra Pedramrazi, Justin Dressel, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi

Mathematics, Physics, and Computer Science Faculty Articles and Research

Ubiquitous noise sources in quantum systems remain a key obstacle to building quantum computers, necessitating the use of quantum error correction codes. Recently, error-correcting codes tailored for noise-biased systems have been shown to offer high fault-tolerance thresholds and reduced hardware overhead, positioning noisebiased qubits as promising candidates for building universal quantum computers. However, quantum operations on these platforms remain challenging, and their noise structures have not yet been rigorously benchmarked to the same extent as those of conventional quantum hardware. In this work, we develop a comprehensive quantum control toolbox for a scalable noise-biased qubit, detuned Kerr-cat qubit, including initialization, …

Asymmetric Positioning Errors In Gnss Time-Series: A Study From Different World Regions, Francesca Silverii, Emilie Klein, Roberto Devoti, Walter Szeliga, Sylvain Michel, Adriano Gualandi, Elisa Trastatti

All Faculty Scholarship for the College of the Sciences

Global Navigation Satellite System (GNSS) plays a fundamental role in monitoring time-dependent ground displacement. However, GNSS daily position time-series can often contain significant outliers, reaching up to several centimetres. These are likely of non-tectonic origin, and, if not properly accounted for, they can significantly impact the accuracy and dependability of the estimation of key parameters for geophysical analyses, such as long-term velocities and transient deformations. Characterizing these outliers can provide information about their possible sources and help us implement mitigation strategies. Asymmetric outliers, that is, those characterized by a primary direction, therefore occurring on one side of the mean time-series, …

Novel R Shiny Tool For Survival Analysis With Time-Varying Covariate In Oncology Studies: Overcoming Biases And Enhancing Collaboration, Yimei Li, Yang Qiao, Fei Gao, Jordan Gauthier, Qiang Ed Zhang, Jenna Voutsinas, Wendy Leisenring, Ted Gooley, Corinne Summers, Alexandre Hirayama, Cameron Turtle, Rebecca Gardner, Jarcy Zee, Qian Vicky Wu

Wills Eye Hospital Papers

PURPOSE: Our study is motivated by evaluating the role of hematopoietic cell transplantation (HCT) after chimeric antigen receptor T-cell (CAR-T) therapy for ALL, a debated topic. Because patients may receive HCT at different times after CAR-T infusion or never, HCT post-CAR-T should be considered as a time-varying covariate (TVC).

METHODS: Standard Cox models and Kaplan-Meier (KM) curves (naïve method) assume that TVC status is known and fixed at baseline, which can yield biased estimates. Landmark analysis is a popular alternative but depends on a chosen landmark time. Time-dependent (TD) Cox model is better suited for TVC although visualizing survival curves …