The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, 2023 Montclair State University, Montclair, New Jersey

#### The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita

*Journal of Humanistic Mathematics*

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, 2023 Benedictine University

#### Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

*Journal of Humanistic Mathematics*

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, 2023 Eckerd College

#### Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

*Journal of Humanistic Mathematics*

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

The Nothing That Really Matters, 2023 J. Selye University, Komárno, Slovakia

#### The Nothing That Really Matters, Szilárd Svitek

*Journal of Humanistic Mathematics*

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …

The Use And Development Of Mathematics Within Creative Literature, 2023 University of St Andrews

#### The Use And Development Of Mathematics Within Creative Literature, Toby S C Peres

*Journal of Humanistic Mathematics*

This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted, and while many examples exist that clearly show an attempt to disperse mathematical ideas, with Lewis Carroll, OuLiPo and ancient poetry considered, the argument that the sole purpose of the writings was for the sake of mathematical development is not clear-cut.

The Genesis Of A Theorem, 2023 Villanova University

#### The Genesis Of A Theorem, Osvaldo Marrero

*Journal of Humanistic Mathematics*

We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it …

Where Do Babies Come From?, 2023 Federal University of Bahia

#### Where Do Babies Come From?, Marcio Luis Ferreira Nascimento

*Journal of Humanistic Mathematics*

According to European folklore, popularized by a fairy tale, storks are responsible for bringing babies to new parents. This probably came from observation in certain European countries, such as Norway, Netherlands or Germany, that storks nesting on the roofs of households were believed to bring good luck, as the possibility of new births. People love stories, but correlation simply means that there is a relationship between two factors that tells nothing about the direction of said relationship, if any. Another possibility is simple coincidence. Let us say that it’s possible that one factor causes another. It’s also possible that the …

Teaching Mathematics After Covid: A Conversation Not A Discussion, 2023 Brock University

#### Teaching Mathematics After Covid: A Conversation Not A Discussion, Wendy Ann Forbes, Joyce Mgombelo

*Journal of Humanistic Mathematics*

Inspired by Brent Davis' conceptualization of listening and conversation in his book *Teaching Mathematics: Toward a Sound Alternative, *we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversation that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful …

Human-Machine Collaboration In The Teaching Of Proof, 2023 University of Toronto

#### Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan

*Journal of Humanistic Mathematics*

This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP *Lean* has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using *Lean* is that …

A Classification Of Musical Scales Using Binary Sequences, 2023 University of Alberta

#### A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen

*Journal of Humanistic Mathematics*

Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three? Here we show that a mathematical classification can be used to identify these scales as representatives of certain *scale families*. Moreover, the classification reveals another scale family, which is much less known: the *harmonic major scale*. We find that each scale family contains exactly seven scales, which include the modes (*dorian*, *phrygian*,...) and other scales such as the *Romanian*, …

The Merchant And The Mathematician: Commerce And Accounting, 2023 Università di Firenze, Italy

#### The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa

*Journal of Humanistic Mathematics*

In this article we describe the invention of double-entry bookkeeping (or *partita doppia*as it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.

The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, 2023 School of Foreign Languages, University of Electronic Science and Technology of China

#### The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani

*Journal of Humanistic Mathematics*

When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely perceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and …

From A Doodle To A Theorem: A Case Study In Mathematical Discovery, 2023 Harvard University

#### From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm

*Journal of Humanistic Mathematics*

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical …

Where Does Mathematics Come From? Really, Where?, 2023 Claremont McKenna College

#### Where Does Mathematics Come From? Really, Where?, Mark Huber, Gizem Karaali

*Journal of Humanistic Mathematics*

No abstract provided.

Front Matter, 2023 Claremont Colleges

Translation Of: Familles De Surfaces Isoparamétriques Dans Les Espaces À Courbure Constante, Annali Di Mat. 17 (1938), 177–191, By Élie Cartan., 2023 College of the Holy Cross

#### Translation Of: Familles De Surfaces Isoparamétriques Dans Les Espaces À Courbure Constante, Annali Di Mat. 17 (1938), 177–191, By Élie Cartan., Thomas E. Cecil

*Mathematics Department Faculty Scholarship*

This is an English translation of the article "Familles de surfaces isoparamétriques dans les espaces à courbure constante" which was originally published in Annali di Matematica 17, 177–191 (1938), by Élie Cartan.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in French. All references should be made to the original paper.

**Mathematics Subject Classification Numbers: 53C40, 53C42, 53B25**

Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, 2023 The University of Texas Rio Grande Valley

#### Combinatorial Identities Associated With A Bivariate Generating Function For Overpartition Pairs, Atul Dixit, Ankush Goswami

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function p(n). Using a result of Shimura we also relate …

Coloring Complexes And Combinatorial Hopf Monoids, 2023 The University of Texas Rio Grande Valley

#### Coloring Complexes And Combinatorial Hopf Monoids, Jacob A. White

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

We generalize the notion of a coloring complex of a graph to linearized combinatorial Hopf monoids. We determine when a linearized combinatorial Hopf monoid has such a construction, and discover some inequalities that are satisfied by the quasisymmetric function invariants associated to the combinatorial Hopf monoid. We show that the collection of all such coloring complexes forms a linearized combinatorial Hopf monoid, which is the terminal object in the category of combinatorial Hopf monoids with convex characters. We also study several examples of combinatorial Hopf monoids.

Exact Parallel Waves In General Relativity, 2023 Massachusetts Institute of Technology

#### Exact Parallel Waves In General Relativity, Cian Roche, Amir Babak Aazami, Carla Cederbaum

*Mathematics*

We conduct a review of the basic definitions and the principal results in the study of wavelike spacetimes, that is spacetimes whose metric models massless radiation moving at the speed of light, focusing in particular on those geometries with parallel rays. In particular, we motivate and connect their various definitions, outline their coordinate descriptions and present some classical results in their study in a language more accessible to modern readers, including the existence of “null coordinates” and the construction of Penrose limits. We also present a thorough summary of recent work on causality in pp-waves, and describe progress in addressing …

A Stronger Strong Schottky Lemma For Euclidean Buildings, 2023 The Graduate Center, City University of New York

#### A Stronger Strong Schottky Lemma For Euclidean Buildings, Michael E. Ferguson

*Dissertations, Theses, and Capstone Projects*

We provide a criterion for two hyperbolic isometries of a Euclidean building to generate a free group of rank two. In particular, we extend the application of a Strong Schottky Lemma to buildings given by Alperin, Farb and Noskov. We then use this extension to obtain an infinite family of matrices that generate a free group of rank two. In doing so, we also introduce an algorithm that terminates in finite time if the lemma is applicable for pairs of certain kinds of matrices acting on the Euclidean building for the special linear group over certain discretely valued fields.