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Articles 1 - 30 of 49
Full-Text Articles in Physical Sciences and Mathematics
Cookie(X) = 1/2, Lawrence M. Lesser
Cookie(X) = 1/2, Lawrence M. Lesser
Journal of Humanistic Mathematics
This poem applies the concept of expected value, denoted E(X), to the context of any limited resources two parties desire. Usually, "you divide, I choose" keeps pieces equal enough to preempt charges of unfairness. But if one piece is much larger, many distrust the unbiased (in expected value) process of a coin flip giving each person the same chance at the bigger piece and the same cookie amount on average: E(X) = (1/2)p + (1/2)(1-p) = 1/2
Ahab's Mercy, David Sheskin
Ahab's Mercy, David Sheskin
Journal of Humanistic Mathematics
A tale in which Captain Ahab and his chief mate Starbuck confront a classic problem in probability theory: the Monty Hall Problem.
Zeno Of Elea: A Dichotomy, Joseph Chaney
Zeno Of Elea: A Dichotomy, Joseph Chaney
Journal of Humanistic Mathematics
This two-part poem interprets Zeno's paradoxes as dimensions of a paradoxical view of reality.
I Am A Math Professor, Cacey L. Wells
I Am A Math Professor, Cacey L. Wells
Journal of Humanistic Mathematics
Original poem depicting the life of a math professor.
Elephant In The Room, Sabrina Sixta
Elephant In The Room, Sabrina Sixta
Journal of Humanistic Mathematics
This poem tries to express the difficulty of staying focused on one's research when there is so much turmoil in the world.
Infinity, Holly Wilson
Ultrafilters, Klaas Pieter Hart
Ultrafilters, Klaas Pieter Hart
Journal of Humanistic Mathematics
5-7-5 musings on ultrafilters.
Her X'S And Y'S: Limericks About Women Mathematicians, Marion D. Cohen
Her X'S And Y'S: Limericks About Women Mathematicians, Marion D. Cohen
Journal of Humanistic Mathematics
This poetry folder is just what its title says, limericks about women mathematicians. A few of them I’ve known personally, most not. There are, of course, many many many other women mathematicians; even though I write limericks prolifically, I could never finish writing about them all!
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani
Journal of Humanistic Mathematics
Mathematics plays an important role in the linguistic structure of artificial in- telligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because al- gorithms, through AI, interfere with the thought of those who interact with …
Beauty Of Life In Dynamical Systems: Philosophical Musings And Resources For Students, Soumya Banerjee, Joyeeta Ghose, Tarakeswar Banerjee, Kalyani Banerjee
Beauty Of Life In Dynamical Systems: Philosophical Musings And Resources For Students, Soumya Banerjee, Joyeeta Ghose, Tarakeswar Banerjee, Kalyani Banerjee
Journal of Humanistic Mathematics
Information plays a key role in life and in complex biological systems, and dynamical systems underlie and can be used to represent many complex systems. Indeed, dynamical systems and information processing capabilities may be the hallmarks of life-like systems. In this paper we combine dynamical systems with a computational framework to generate art. The framework can be used to generate aesthetically appealing forms of life-like systems. Our work suggests that we may need an ``aesthetic sense'' to recognize life that we have not seen before. We also provide teaching resources for students in schools and undergraduate institutions.
The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post
The Number Systems Tower, Bill Bauldry, Michael J. Bossé, William J. Cook, Trina Palmer, Jaehee K. Post
Journal of Humanistic Mathematics
For high school and college instructors and students, this paper connects number systems, field axioms, and polynomials. It also considers other properties such as cardinality, density, subset, and superset relationships. Additional aspects of this paper include gains and losses through sequences of number systems. The paper ends with a great number of activities for classroom use.
The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson
The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson
Journal of Humanistic Mathematics
In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Journal of Humanistic Mathematics
In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …
One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little
One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little
Journal of Humanistic Mathematics
If the three sides of a triangle ABΓ in the Euclidean plane are cut by points H on AB, Θ on BΓ, and K on ΓA cutting those sides in same ratios:
AH : HB = BΘ : ΘΓ = ΓK : KA,
then Pappus of Alexandria proved that the triangles ABΓ and HΘK have the same centroid (center of mass). We present two proofs of this result: an English translation of Pappus's original synthetic proof and a modern algebraic proof making use of Cartesian coordinates and vector concepts. Comparing the two methods, we can see that while the algebraic …
Teaching Mathematics With Poetry: Some Activities, Alexis E. Langellier
Teaching Mathematics With Poetry: Some Activities, Alexis E. Langellier
Journal of Humanistic Mathematics
During the summer of 2021, I experimented with a new way of getting children excited about mathematics: math poetry. Math can be a trigger word for some children and many adults. I wanted to find a way to make learning math fun—without the students knowing they’re doing math. In this paper I describe some activities I used with students ranging from grades K-12 to the college level and share several poem examples, from students in grades two to eight.
Ekstasen: Love Poetry By Felix Hausdorff, Kimberly Gladman
Ekstasen: Love Poetry By Felix Hausdorff, Kimberly Gladman
Journal of Humanistic Mathematics
Four poems by the mathematician Felix Hausdorff are presented in English translation, together with their German originals and commentary about Hausdorff’s multidisciplinary achievements.
Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe
Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe
Journal of Humanistic Mathematics
In this article we argue that Raphael has hidden a geometric shape called a vesica piscis in his fresco The School of Athens (1510-1511). The vesica piscis, and several findings which can be interpreted as suggesting the presence of a vesica piscis in the fresco, are presented. Several of these suggestions relate to the vesica piscis drawn in the construction of an equilateral triangle in the first proposition of Euclid’s Elements. Based on findings in the fresco, we suggest that the vesica piscis should be interpreted in light of a philosophical and theological controversy which took place in Italy …
The Long Search For Collatz Counterexamples, Oliver K. Clay
The Long Search For Collatz Counterexamples, Oliver K. Clay
Journal of Humanistic Mathematics
Despite decades of effort, the Collatz conjecture remains neither proved, nor refuted by a counterexample, nor formally shown to be undecidable. This note introduces the Collatz problem and probes its logical depth with a test question: can the search space for counterexamples be iteratively reduced, and when would it help?
Students’ Mathematical Learning During The Covid-19 Pandemic, Jessica Mean, Shilpa Dasgupta
Students’ Mathematical Learning During The Covid-19 Pandemic, Jessica Mean, Shilpa Dasgupta
Journal of Humanistic Mathematics
This paper discusses our new approach to assessing students’ learning. This approach includes the use of a final project rather than a final cumulative exam. We suggest that students taking a deep dive into one particular math concept and being able to make connections between that concept and the real world are educational achievements during this pandemic. We also argue that there is value in online learning because students who learn online choose to use library resources and develop their own interests by attending office hours, all of which benefit their learning.
No Simple Formula: Navigating Tensions In Teaching Postsecondary Social Justice Mathematics, Alexa W. C. Lee-Hassan
No Simple Formula: Navigating Tensions In Teaching Postsecondary Social Justice Mathematics, Alexa W. C. Lee-Hassan
Journal of Humanistic Mathematics
Instructors of Social Justice Mathematics (SJM) have shared important insights into the powerful potential of connecting classroom mathematics with authentic data about social justice topics, but they have also warned about the harm such teaching can cause when done poorly. In this article, I consider what is necessary to teach SJM at the postsecondary level. I share research that has supported me in learning to teach SJM and highlight challenges that are particular to doing this work in postsecondary contexts. I then describe my experiences navigating the central tensions of this work while honoring its complexity.
Critical Co-Investigators Of Math Trails: Reflections From A Student And Teacher, Benjamin Dickman, Julia Feinberg
Critical Co-Investigators Of Math Trails: Reflections From A Student And Teacher, Benjamin Dickman, Julia Feinberg
Journal of Humanistic Mathematics
In this article, a K-12 mathematics educator and a recent (2020) high school graduate discuss curricular work related to math trails, which are based around the idea of mathematizing potential discoveries along a physical walk. The intersection of math trails with the realities of schooling amid the COVID pandemic is described, along with ways in which math trail learning has ramified beyond classroom walls. This collaboration serves not only to draw attention to the under-researched topic of math trails, but also to exhibit how students and teachers can, in the language of Freire, work together as critical co-investigators.
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
Journal of Humanistic Mathematics
In 2019, \#DisruptJMM, a Twitter hashtag, began circulating after an Inclusion/Exclusion blog by Dr. Piper H pointing to the need to make commonplace conversations about human suffering in the Joint Mathematics Meetings (JMM). While the \#DisruptJMM hashtag has been used since 2019, the vast majority of use was in the JMM 2020 meetings. Twitter hashtags are used by activists to push forward conversations, join communities around a single idea, and create change. In this article, we draw on frameworks from community building seen in other equity and inclusion advocacy hashtags such as \#GirlsLikeUs [7] to qualitatively code and analyze tweets …
On Definitions Of "Mathematician", Ron Buckmire, Carrie Diaz Eaton, Joseph Hibdon, Katherine M. Kinnaird, Drew Lewis, Jessica Libertini, Omayra Ortega, Rachel Roca, Andrés R. Vindas Meléndez
On Definitions Of "Mathematician", Ron Buckmire, Carrie Diaz Eaton, Joseph Hibdon, Katherine M. Kinnaird, Drew Lewis, Jessica Libertini, Omayra Ortega, Rachel Roca, Andrés R. Vindas Meléndez
Journal of Humanistic Mathematics
The definition of who is or what makes a “mathematician” is an important issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline—both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to highlight, examine, and challenge systemic barriers that exist in certain spaces of the community. This paper analyzes and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, …
Mathematics And Society: Towards Critical Mathematics Research And Education, Tian An Wong, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez
Mathematics And Society: Towards Critical Mathematics Research And Education, Tian An Wong, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez
Journal of Humanistic Mathematics
No abstract provided.
Mathematics And Society, Mark Huber, Gizem Karaali
Mathematics And Society, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
Between Heaven And Earth! A Poem-Collage Pair About Hypatia Of Alexandria, Sarah Glaz, Mark Sanders
Between Heaven And Earth! A Poem-Collage Pair About Hypatia Of Alexandria, Sarah Glaz, Mark Sanders
Journal of Humanistic Mathematics
The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Included as background is a brief discussion on the history and mathematics involved, and a reflection on several landmark locations and some of the relevant imagery appearing in the poem and the collage.
Astor Place Barber, Audrey Nasar
Astor Place Barber, Audrey Nasar
Journal of Humanistic Mathematics
"Astor Place Barber" is a short story about a math professor and a barber. It plays with the logical concept of a paradox via the Barber's Paradox, which, made famous by Bertrand Russell, tells the story of a barber who both shaves himself and does not shave himself.
Locked In Functions: A Short Poem For Robert Langlands, Virgilio A. Rivas
Locked In Functions: A Short Poem For Robert Langlands, Virgilio A. Rivas
Journal of Humanistic Mathematics
This short poem is inspired by Robert Langlands, recipient of the 2018 Abel Prize. The poem tries to sum up in poetic language, as brief but substantial as it can be, the philosophical and rhetorical connotation of his contributions to mathematics, from automorphic forms to number theory, and the famous Langlands programme, among others. Also partly inspired by Edward Frenkel's tribute to Langlands, the book Love and Mathematics, the poem seeks to capture the philosophical beauty of mathematics that privileges the importance of 'functions' over 'passions', consistent with Langlands' purely mathematical side.
Unsolved Haiku, Scott W. Williams
Unsolved Haiku, Scott W. Williams
Journal of Humanistic Mathematics
This poem describes the still unsolved 1937 conjecture of Lloyd Collatz: Do repeated applications of the algorithm described yield the number 1?