Physical Sciences and Mathematics Commons^™

Mathiverse - A Potpourri Of Mathematical Stanzas, Vijay Fafat

Journal of Humanistic Mathematics

A collection of very short verses, mathematical in nature.

Book Review: Zero's Whisper By Tom Petsinis, Sarah Glaz

Journal of Humanistic Mathematics

Tom Petsinis is an internationally acclaimed Australian novelist, playwright, and poet. He also holds a Ph.D. degree in mathematics and works as a mathematical adviser at Deakin University, Melbourne. Zero’s Whisper, Petsinis’ tenth poetry collection, offers a rich blend of the literary and the mathematical. The collection, comprising of over one hundred fourteen-line poems, is divided into nine sections, each of which considers a different aspect of a world steeped in mathematics and poetry. This review aims to provide a taste of the poetry and the themes included in the book. To discover all its hidden delights, one needs to …

Compare Problems: Complexity In Content And Language, Gladys Krause

Journal of Humanistic Mathematics

When learning to teach mathematics in elementary school, pre-service teachers (PSTs) spend considerable time studying word problems. Here I present a resource I have created for my mathematics methods course in order to engage PSTs in learning about these problems and to support them in identifying these problem types.

Let’S Teach More Accurate And Inclusive History! The Case Of Islamic Contributions To Mathematics And Science, Nuh Aydin

Journal of Humanistic Mathematics

Schools commonly teach a history of mathematics and science that is Eurocentric. This selective version of the history of science, called Classical Narrative by some, is rooted in colonial times and mindset, and has reinforced certain negative opinions about other cultures. It ignores or downplays contributions to mathematics and sciences from non-western civilizations, and falsely attributes many scientific discoveries to European scholars. Medieval Islamic Civilization, which had strong connections to Renaissance Europe, serves as a clear example of how this narrative is distorted. Based on research on primary sources since the middle of the 20th century, we now know that …

From Shudu [Sudoku 數獨] To Dushu [Learning Of Mathematics 讀數]?, Man Keung Siu

Journal of Humanistic Mathematics

The puzzle game Sudoku has been popular for over two decades, and even at one time became a craze for the public. This paper will briefly describe what the game is, a little bit of its history, and how to play it, but will leave the details to the many published books about the game. Some interesting and difficult mathematical problems relevant to the game will be highlighted, again leaving the detailed discussion to specific books published on this issue. The main point the paper tries to focus on is a discussion on the cognitive and the psychological aspects of …

The Fake Mathematical Mindsets Of Preservice Teachers, Carmen M. Latterell

Journal of Humanistic Mathematics

Many students have a fixed mindset, as do some teachers. Recently I accidentally discovered that most of the preservice elementary teachers in my class were faking their mindset and pretending that they had a growth mindset. This raises a variety of questions, such as, will this follow a fake it until you make it track?

Small Number And The Old Game, Veselin Jungic

Journal of Humanistic Mathematics

Through a conversation between Small Number and his Auntie, this article describes the Throwing Game, a Haida tradition recorded by John Swanton in 1905. Several mathematical concepts that may be associated to the game are mentioned.

Examples Of Mathematics Personified, Amenda N. Chow

Journal of Humanistic Mathematics

Synesthesia is a cognitive condition in which multiply senses are stimulated at once. There are different types of synesthesia. For example, in a documented study [9], a person with synesthesia when considering the number three associates it as a male and a jerk. This association is persistent, always the same and automatic. Presented here are a variety of examples about mathematics in personified form. These examples focus on using personification as a way to better understand and appreciate mathematics.

Math Anxiety And Shame Exemplified On The Reality Show Survivor, James Drimalla, Dru Horne

Journal of Humanistic Mathematics

In an episode of season 45 of the reality show Survivor, three contestants competed in a challenge involving mathematics. In their reflections and responses to the challenge, the contestants discussed feelings of anxiety, fear, and shame. In this article, we describe (a) the challenge, (b) the three contestants’ attempts to complete the challenge and their responses to the challenge, (c) responses to the challenge in the media, and (d) relevant details of our personal experiences and related backgrounds. We then discuss themes of math anxiety, shame, and virtues, and encourage leaders in mathematical spaces to place a higher value on …

Introducing The Linear Poem, Cristian Ramirez Rodriguez

Journal of Humanistic Mathematics

In this article I introduce the linear poem, a poetic form I developed in fall 2023 as a pedagogical tool for high-school students. The linear poem is a poem which represents an integer valued linear function, treating the line numbers as inputs and the linguistic units in a line as outputs. Two examples of linear poems are given as well as the steps taken to produce them. By interpreting poetic forms as integer-valued functions as is done in this article, interdisciplinary pedagogy can be achieved, allowing educators and students to express mathematical ideas such as slope-intercept form in a creative …

A Dualistic Interpretation Of Mathematical Creation Through Art And Argumentation, Sofia Almpani, Petros Stefaneas, Mihir Chakraborty

Journal of Humanistic Mathematics

Creativity, informal reasoning and dynamic exchange of ideas form the pulsating heart of mathematical creation. In this approach, the concept of a mathematical object surpasses conventional boundaries of formal presentation, as they also encompass the intention to prove, significant creative stages within the proving, and the overall experience of prover's journey, which may involve arguments, debates, discovery insights, aesthetic visualizations, and narrative elements. In this paper we present two conceptual frameworks, namely Argumentation-based Proof-Events Calculus (APEC) and Mathematical RUPAs, in order to provide distinct yet interconnected perspectives on informal thinking, knowledge creation, and proving in mathematics. Following the two perspectives, …

On Gödel’S Incompleteness Theorem, David Pierce

Journal of Humanistic Mathematics

Gödel’s Incompleteness Theorem is about the logic of mathematics. It is that a certain mathematical structure is so rich that its theory cannot be completely axiomatized. This means there will always be true statements about the structure that cannot be proved as theorems from previously given axioms. To give meaning to this conclusion, we review some examples of mathematical theorems, and their proofs, in geometry, algebra, and logic; we also give an example of a structure that is so simple (while still being interesting) that its theory can indeed be completely axiomatized. First we look at a couple of popular …

Exploring Commutativity In A Hindi Language Classroom, Kumar Gandharv Mishra

Journal of Humanistic Mathematics

Commutativity is an important concept in mathematics. However, not much emphasis is given to it in the elementary or secondary school curriculum, as there is a lack of interesting noncommutative examples at this level. Since most examples of binary operations provided deal with numbers, commutativity appears trivial. In this article we offer an interesting example of noncommutativity that is familiar to Indian school children from a different context. Students in India study a chapter based on the joining of vowels in Hindi grammar. This process is analogous to producing commutative as well as noncommutative operations. When we bring in mathematical …

Revisiting A 19th Century Vector Algebra Book, Olcay Coskun, Alp Eden, Ersin Karabudak

Journal of Humanistic Mathematics

Hidden gems of mathematics can be recovered when one digs into what might seem an obscure text. In 1882, military officer Vidinli Hüseyin Tevfik Pasha published a book on vector algebra titled Linear Algebra. In this article we revisit the second edition of this book, emphasizing the special multiplication that we call the ’v-product’. This product has both geometric and algebraic characteristics. We attempt to clarify its relationship with complex and quaternion multiplication both geometrically and algebraically. The resulting algebra is called the Vidinli algebra. This algebra admits a Lie algebra structure that gives rise to Heisenberg algebra. We introduce …

Memes As An Effective Approach To Increase Public Engagement With Mathematical Concepts, Juan M. Romero, Carlos Trenado

Journal of Humanistic Mathematics

A meme is a graphical concept or cultural item that is disseminated via the Internet, often through social media platforms. Memes serve as a mechanism for replicating cultural traits by incorporating aspects of cultural mutation and evolution. The potential of memes in learning and education has been emphasized in several recent studies. The present article examines the impact of memes in increasing public engagement with mathematics and mathematical concepts. By focusing on memes that exhibit specific attributes—such as emotional facial expressions of recognizable human characters and dialogues emphasizing the usefulness or beauty of a mathematical concept—we observe a significant increase …

Graphical Timetables As A Real-Life Example Of Different Representations Of Functions, Olav G. Imenes

Journal of Humanistic Mathematics

This paper examines 203 pre-service teachers' reactions and learning when they were introduced to a real-life situation in which it is natural to publish officially both graphs and tables of a given function: the situation of operating a railway. I found that almost all the pre-service teachers managed the easiest tasks, like calculating speeds, distances, and time for train represented by graphs. However, the more complicated tasks, which required interpretations of the graphs and tables, such as planning for a delayed train, finding which trains were locals, freight trains etc., were more difficult for them to grasp. There were few …

Evaluating Methods Used To Quantify Racial Segregation, Sarah Cannon, Zarina Dhillon

Journal of Humanistic Mathematics

Racial segregation has long been a problem in communities across the United States. One approach to help understand such an important issue is to attempt to describe it quantitatively. Many metrics have been developed, all with various strengths and weaknesses, but none fully capture the nuances of this complicated issue. This work provides an overview of four of the mathematical approaches that have been developed to study segregation, explains how they function using small examples, and compares and contrasts their effectiveness in various situations. We then focus on segregation in Los Angeles (LA) County, including a detailed exploration of the …

A Practical Rule Of Divisibility By 7 In Uqlīdisī’S Kitāb Al-Fuṣūl Fī Al-Ḥisāb Al-Hindī, Müjdat Takıcak, Mertkan Şimşek

Journal of Humanistic Mathematics

There are many known examples of divisibility rules in modern mathematics. However, some of these rules are far from being practical, such as the current divisibility rule by 7. A far more useful method can be found in the work of the tenth-century Islamic mathematician Abū al-Ḥasan al-Uqlīdisī (d. 980), who proposed a divisibility rule for 7 in his treatise Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Compared to modern techniques, Uqlīdisī’s rule is both simpler and more practical. This article (re)introduces this rule, and provides an exposition of the mathematical reasoning that underpins it.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

What Can Mathematics Do For Us?, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Modeling Covid-19 Spread And Effects Of Non-Pharmaceutical Interventions On A College Campus, Jakob Kotas, Priscilla Perey Ratonel

CODEE Journal

We consider an extension to the classical SIR compartmental model from mathematical epidemiology as applied to the spread of COVID-19 on a college campus. While the classical SIR model does not allow for recovered individuals to lose immunity, we alter the equations to allow for such (due to the rise of new variants), leading to a SIRS-type model. We study the system of ODEs analytically and through numerical simulation. Finally we discuss a quantitative approach for how college administrators can decide when to implement stricter non-pharmaceutical interventions (social distancing, mask mandates, quarantine, etc.) to eradicate the infection from the campus …

For Chow Variety Try This New Dessert Recipe, Jane P. Sheldon

Journal of Humanistic Mathematics

A positive addition to any dinner table or social function, this baked good can be served plane or à la mode.

Integration Bar, Erik Talvila

Journal of Humanistic Mathematics

In this humourous story, the narrator is dragged by their friend to a crazy bar for a late night of wild drinking and dancing. Except, the drinking is replaced with computing integrals.

Constanto Mysterium - A Paradise Of Shifting Constants, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians speak of constants of mathematics. Some of these constants are known to high-heavens. Some remain hidden in the obscurity of erudition. And to be frank, while every real number is a mathematical constant, we don’t know much about most of them (is not the set of transcendental numbers incommensurable without us knowing or understanding very many of them?).

So what elevates some constants above others? Is this elevation just a measure of the ignorance of mathematicians who have explored but a small patch of an infinite quilt, a case of six wise men trumpeting the – well, the trumpet …

Welcome 2025—The Year Of A Magical Number, Md Sadikur Rahman

Journal of Humanistic Mathematics

This is a poem to welcome the new year 2025 and note its relevance to mathematics.

A Ramsey Theory Essay: The Dinner Party, Ryan Coghill

Journal of Humanistic Mathematics

This is a poem inspired by Ramsey’s theorem. Its main characters are; Frank Ramsey, Issai Schur, Richard Rados, Bertel van der Waarden, Ronald Graham and Paul Erdos, some of the pioneers of the field of Ramsey theory. There has been care put into each paragraph so that it’s lines can be viewed as though they were nodes on a graph which share traits with each other of rhyme, theme and length which can be paired in 2 states, sharing and unique in such a way that one might find coloured graph edges when working in the field of Ramsey theory.

Math Is A Tiger And A Pecan, William Cocke

Journal of Humanistic Mathematics

Using perfect secrecy and the ability to identify gibberish in a given language, we encode two poems in one. This allows for a single cipherpoem to have multiple plainpoems associated with it. The result is a form of superposition where neither poem is the more correct interpretation than the other.

The poem presented is about two distinct aspects of mathematics: the tiger to be sought after and hunted; or a pecan that we have surrounded but cannot crack open.

My Academic Life -- A Poem, Sonja Petrovic

Journal of Humanistic Mathematics

No abstract provided.

Belonging, Lawrence M. Lesser

Journal of Humanistic Mathematics

No abstract provided.

What Happened When I Took Calculus For The First Time At Age 47, Britt Kaufmann

Journal of Humanistic Mathematics

These five poems are inspired by being in high school math classes and could be used in the classroom for cross-curricular enrichment.