Mathematics Commons^™

The Mathematics Of The Astrolabe And Its History, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa

Journal of Humanistic Mathematics

In this article we trace the scientific and cultural history of the astrolabe, a mechanical instrument used in the past for astronomical measurements and navigational purposes. The story of the astrolabe is interesting from several points of view, since it intertwines mathematical developments, geographical explorations, changing worldviews, and different cultures and civilizations. In our explorations we move from the early understanding of the world due to the Greeks, to the loss of their work, its rediscovery, the reception of Arab thinkers in Western natural philosophy, and, finally, to the new European culture that emerged with the end of the Middle …

College Students’ Images Of Mathematicians And Mathematical Careers, Katrina Piatek-Jimenez, Miranda Nouhan, Michaela Williams

Journal of Humanistic Mathematics

In this paper we report our findings of college students’ images of mathematicians and we reflect on different methodologies used to assess this information. The study reported in this paper was conducted in two stages. During the first stage, we asked 179 college students to “draw a mathematician” and also asked them to list five characteristics and five careers for a mathematician. In the second stage of the study, we conducted four focus group interviews with a total of twelve college students. During the focus group interviews, we showed the students 16 photos of real people and asked them to …

Engaging The Paradoxical: Zeno's Paradoxes In Three Works Of Interactive Fiction, Michael Z. Spivey

Journal of Humanistic Mathematics

For over two millennia thinkers have wrestled with Zeno's paradoxes on space, time, motion, and the nature of infinity. In this article we compare and contrast representations of Zeno's paradoxes in three works of interactive fiction, Beyond Zork, The Chinese Room, and A Beauty Cold and Austere. Each of these works incorporates one of Zeno's paradoxes as part of a puzzle that the player must solve in order to advance and ultimately complete the story. As such, the reader must engage more deeply with the paradoxes than he or she would in a static work of fiction. …

What Gets Checked At The Door? Embracing Students' Complex Mathematical Identities, Jennifer L. Ruef

Journal of Humanistic Mathematics

Identity formation is complex, ongoing, and context specific. To be successful in mathematics classes, students must negotiate and navigate the normative identity of the class--what counts as being "good at math" (Cobb, Gresalfi & Hodge, 2009). Within the constraints of normative identity, students must also negotiate a personal doer-of-math identity: who they are within the context of this particular mathematics class. When students are compelled to suppress key aspects of their identity in order to accommodate the normative identity of the class cognitive bandwidth for learning may be impeded (Steele, 1997). Conversely, when students are guided in braiding individual identity …

John Cheever's Story "The Geometry Of Love", Robert Haas

Journal of Humanistic Mathematics

Though John Cheever was a leading writer of short fiction, his story “The Geometry of Love” has received little prior literary or mathematical comment. In this essay it is read, against the background of Cheever’s own troubled life and marriage, as a Don Quixote – like search, explicitly following the model of Euclidean geometry, and at times wildly funny, for an ideal world of truth and happiness.

Starting Our Decennial, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Third Voices Conference On Teaching Stem With Music, September 22-23, 2019, Lawrence M. Lesser

Journal of Humanistic Mathematics

The third annual VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song; https://www.causeweb.org/voices/) conference will be held online September 22-23, 2019. Chaired by Tiffany Getty, this conference will explore the use of song to teach STEM (science, technology, engineering, and mathematics) at the postsecondary (or secondary) level.

How To Bake A Theorem, Cache Dexter

Journal of Humanistic Mathematics

We bake bread to satisfy our hunger, and we prove theorems to satisfy our hunger for knowledge and existence. Here I explore this analogy.

Tartaglia Re-Imagined, Aja Juola

Journal of Humanistic Mathematics

Niccolo Fontana wrote that he wore a beard because he feared his appearance was monstrous. No one should ever feel such shame about their physical appearance so I figured after all these years I would tell him to bare his scars proudly as a reminder of what he had endured and the life he led.

Applied Scientific Demiurgy I – Entrance Examination Information Sheet, Mario Daniel Martín

Journal of Humanistic Mathematics

This document provides all the required information needed by aspiring demiurges to sit the entrance examination for the foundation course Applied Scientific Demiurgy I in the scientific stream of the Bachelor of Applied Demiurgy at the Topological Hyper-university of Technological Cosmology.

Our Binary World, Simona Carini

Journal of Humanistic Mathematics

A poem about counting in binary, life, and love.

Tuesday, Ursula Whitcher

Journal of Humanistic Mathematics

"It's Tuesday, and the week's no longer new . . ." This poem's form is taken from the structure of the field with seven elements: the meter, in iambs, follows a pattern based on 5, 4, 6, 2, 3, the nontrivial values taken by powers of 5 (mod 7) as it generates the group of units of the field.

What Is Math?, Christopher Ryan Loga

Journal of Humanistic Mathematics

Here is presented a poem examining what math is and is not and the conclusions (if any) we can draw as such.

A Life Of Equations Shifting To A Life Of Words, Thomas R. Willemain

Journal of Humanistic Mathematics

As my technical life diminishes, my writing life increases. Since 2017 I have been writing, first a memoir of my time in the Intelligence Community, then poetry and flash fiction.

One of the missions I have assigned to my poetry is to expose to `regular' people the inner life of the mathematical person. The poems in this poetry folder develop three themes. "Formulations'' pokes a bit of fun at the bloated (and in this case almost musical) titles that can grow from our research; more seriously, it documents the change in self-definition that flows from recognizing the inevitable drift away …

Book Review: The Seduction Of Curves By Allan Mcrobie, Hans J. Rindisbacher

Journal of Humanistic Mathematics

This review emphasizes, as does the compelling and beautiful book, The Seduction of Curves by Allan McRobie, the “lines of beauty” that link art and mathematics. McRobie and his collaborator on the indispensable visuals of the volume, Helena Weightman, succeed admirably in connecting theoretically and visually the mathematical field of singularity or catastrophe theory and its graphical representations on the one hand and the seemingly intersecting lines around the volumes of the human body in the artistic representation of the nude. This book thus constitutes a creative and illuminating overlap of mathematics and art that lets the practitioners on both …

Book Review: What Is A Mathematical Concept? Edited By Elizabeth De Freitas, Nathalie Sinclair, And Alf Coles, Brendan P. Larvor

Journal of Humanistic Mathematics

This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms ‘mathematical’ and ‘concept’. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question ‘what is a mathematical concept?’ from the philosophy of mathematics. This review comments …

Ducci’S Four-Number Game: Making Sense Of A Classic Problem Using Mobile Simulation, Lingguo Bu

Journal of Humanistic Mathematics

Ducci’s Four-Number Game is a classic mathematical puzzle appealing to a wide audience for its procedural simplicity, mathematical richness, and aesthetic values. This article first describes a few activities appropriate for school students and mathematics teachers to make sense of the intriguing behavior of the game. Then, using a mobile simulation, we delve into the lengths of the Four-Number Game and the corresponding probability distribution. The Ducci number game is playful, engaging, and full of mathematical surprises.

What Are The Odds At The Russia 2018 Fifa World Cup?, Gunhan Caglayan

Journal of Humanistic Mathematics

In this note we explore the group stage competition format in a standard FIFA World Cup Soccer Championship group phase. The group stage involves thirty-two teams divided into eight groups of four teams each, based on a draw that takes the national teams’ seeding and geographical location into consideration. Each of the four teams in a given group is scheduled to play one match against every other team in the same group. Upon the completion of six games in each of the eight groups (for a total of 48 games), the top two highest scoring teams (the winner and the …

Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge

Journal of Humanistic Mathematics

Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.

Everyman's Climb, Charles A. Coppin

Journal of Humanistic Mathematics

Hal and Verity represent two different philosophies of learning, one used by most of us. In today’s world, authentic teaching is indeed a heroic act, but may not be the most popular. This piece draws distinctions between these choices, each time we teach a course, each day we walk into the classroom, and even when working with an individual student; they are ever present.

Differential Equations Of Love And Love Of Differential Equations, Isaac Elishakoff

Journal of Humanistic Mathematics

In this paper, simple ordinary differential equations are discussed against the background of William Shakespeare’s Romeo and Juliet. In addition, a version of this relationship in a somewhat opposite setting is considered. It is proposed that engineering mathematics courses include this topic in order to promote additional interest in differential equations. In the final section it is shown that vibration of a single-degree-of-freedom mechanical system can be cast as a love-hate relationship between its displacement and velocity, and dynamic instability identified as a transition from trigonometric love to hyperbolic.

Beyond The Classroom: Mathematics In Service, Jeana Mastrangeli

Journal of Humanistic Mathematics

Mathematical expertise demands effective thinking and learning methods, and these techniques transfer well to other domains. In this article, I discuss how my own training as a pure mathematician influenced my performance in three disparate domains: electrical engineering, art appreciation, and learning Italian. In electrical engineering, the focus is on how mathematical reasoning and thinking processes impact knowledge acquisition and problem solving. Appreciating and analyzing art raises the question, “How do we know for certain?” Acquiring fluency in another language is akin to gaining mathematics proficiency, and here, I explore the human side of persistence. The article combines narrative, reflection, …

Mathematics Students As Artists: Broadening The Mathematics Curriculum, Marshall Gordon

Journal of Humanistic Mathematics

Mathematics has often been referred to as an art. For some it is “the purest of the arts”, where the mathematicians’ art is “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations”. Yet with classroom time given primarily to “covering the curriculum”, testing, and practicing problem-solving procedures, students’ opportunities to appreciate the aesthetic dimension of mathematics are often limited. To promote a responsive environment in an effort to enable students to become artists of their own mathematics experience, I consider in this paper two facets of the mathematics classroom. Content-wise I make the argument …

A Few Firsts In The Epsilon Years Of My Career, Heidi Goodson

Journal of Humanistic Mathematics

In this essay, I describe the unexpected ways I achieved some milestones in the early years of my career.

A Graph-Based Analysis Of Anton Chekhov’S Uncle Vanya, Stanislaw Zawislak, Jerzy Kopeć

Journal of Humanistic Mathematics

We analyze the famous Anton Chekhov play Uncle Vanya by means of graph theory. Moreover, we make the ‘brave’ suggestion that Chekhov might have used graphs to represent the plot of the play and the relationships between characters. Our analysis also includes the analysis of a specific performance of the play held in Bielsko-Biała which differs slightly from the original script. The differences between the two versions are traced via graph-based analyses. When a first round of clique assignments did not give much insight we transformed them via a sequence of operations on consecutive graphs. The final graphs obtained this …

Mathematics Versus Statistics, Mindy B. Capaldi

Journal of Humanistic Mathematics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.

Finding Beauty: A Case Study In Insights From Teaching Developmental Mathematics, Victor Piercey, Geillan Aly

Journal of Humanistic Mathematics

As mathematicians, we often fail to appreciate the opportunities open to us when we teach developmental mathematics. One such opportunity is that we may deepen our understanding of mathematics that we have taken for granted. This paper contains a brief case study concerning what we have learned about operations, inverses, and exponents in the process of teaching beginning algebra. Our inquiry takes us from student questions about signed numbers, through the category of rings, to the world of Lie groups and Lie algebras.

Public Recognition And Media Coverage Of Mathematical Achievements, Juan Matías Sepulcre

Journal of Humanistic Mathematics

This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathematics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians. We provide examples of recognition accorded by institutions, societies, schools, communities, academies, and the public in general to these mathematicians.

Telling Women's Stories: A Resource For College Mathematics Instructors, Sarah Mayes-Tang

Journal of Humanistic Mathematics

Stereotypes about mathematicians that conflict with ``traditionally feminine" identities are widely held by people from middle-school-age onwards, and can influence their participation in mathematics and related fields. Simply being exposed to women in mathematics is not enough to change students' perceptions of mathematicians, and may even decrease girls' interest in mathematics. This paper proposes a storytelling strategy to help change students' perceptions of mathematicians. It includes several activities for intentionally incorporating women's stories into the post-secondary classroom and a list of resources for finding existing powerful stories. The diverse stories of women mathematicians, including details of their personal lives and …