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Articles 91 - 120 of 1981
Full-Text Articles in Mathematics
Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems, Gracie Crooks, F. Ayça Çetinkaya
Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems, Gracie Crooks, F. Ayça Çetinkaya
CODEE Journal
We investigate the inverse problem of identifying damping and stiffness parameters in one-dimensional damped oscillatory systems governed by second-order differential equations. Focusing on mass–spring–damper models, we analyze the qualitative behavior of solutions across underdamped, critically damped, and overdamped regimes, and derive explicit conditions for parameter recovery based on time-domain observations such as equilibrium crossings and turnaround points. Two numerical estimation methods are developed and compared: a finite-difference least-squares approach based on central difference approximations, and a finite element formulation derived from a variational framework using piecewise linear basis functions. Computational experiments using synthetic data assess the accuracy, stability, and noise …
Project-Based Learning With Odes: Modeling Straw Rocket Motion With Air Resistance, Viktoria Savatorova, Ethan Dyer, Aleksei Talonov
Project-Based Learning With Odes: Modeling Straw Rocket Motion With Air Resistance, Viktoria Savatorova, Ethan Dyer, Aleksei Talonov
CODEE Journal
This paper presents a hands-on project that guides students through building and validating a mathematical model of projectile motion. The project starts with the idealized case of motion under gravity without air resistance and then introduces air drag : first as a linear force, and then as a nonlinear quadratic force, with the Reynolds number providing the justification for the quadratic model. Students perform experiments with vertical and angled launches, capturing and analyzing motion data using video analysis software. Vertical launch data allows parameter estimation via least squares fitting of the nonlinear drag model, yielding values for initial velocity and …
Interlace: A Journal Of Mathematics And Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro
Interlace: A Journal Of Mathematics And Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro
Journal of Humanistic Mathematics
Interlace: A journal of mathematics and fiber arts is a peer-reviewed, open-access completely free journal devoted to publishing high-quality original research at the intersection of mathematics and fiber arts. The journal is now accepting submissions.
Sudoku Grids, David Sheskin
Sudoku Grids, David Sheskin
Journal of Humanistic Mathematics
Ten images depicting numerical grids of the mathematical logic puzzle Sudoku are presented. The digit values in each puzzle are represented on either domino tiles, postage stamps, mah-jong tiles, or playing cards.
The Unending Constant, Christopher Banyas
The Unending Constant, Christopher Banyas
Journal of Humanistic Mathematics
No abstract provided.
Totality Fractal, Heather L. Cook
Totality Fractal, Heather L. Cook
Journal of Humanistic Mathematics
This fractal was inspired by the Total Solar Eclipse on April 8, 2024. Here, the sun and the moon are represented when in totality.
Euclidean Vision (A Poem), Joseph Chaney
Euclidean Vision (A Poem), Joseph Chaney
Journal of Humanistic Mathematics
"Euclidean Vision" is a short poem that evaluates geometry from a humanistic perspective, focusing partly on its pleasures. Geometry gives us the pleasing assurance of certainty. It does this through the radical abstraction of space and form, which makes possible a completeness of mathematical vision based on axioms. It's this purity that guarantees a knowledge that "can go on forever." In the end, the poem points to the wonderful freedom that geometry and other mathematical disciplines give us in the midst of difficult and confusing lives. In its beauty and universality, geometry stands as an eternal aspect of the human …
Dream Series, Jim Wolper
Dream Series, Jim Wolper
Journal of Humanistic Mathematics
Dream Series converge to numbers we cannot analyze. They exist, like dreams, but resist attempts to put them into order.
Solving For..., Jan B. Shafer
Solving For..., Jan B. Shafer
Journal of Humanistic Mathematics
This poem is about an appreciation of mathematics and its relationships to people and nature.
When I Was One-In-Twenty, Daniel Kowalczyk
When I Was One-In-Twenty, Daniel Kowalczyk
Journal of Humanistic Mathematics
A poem by A.E. Housman inspired the engineer John R. Pierce to feel awe in the technological progress of telecommunications. Tangentially, Housman also evoked a strong emotion in me when making use of statistical p-values.
Found Poem By Abraham De Moivre, Richard Delaware
Found Poem By Abraham De Moivre, Richard Delaware
Journal of Humanistic Mathematics
No abstract provided.
Mathiverse - A Potpourri Of Mathematical Stanzas, Vijay Fafat
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.