Mathematics Commons^™

Quantitative Literacy, Thomas L. Moore

Journal of Humanistic Mathematics

No abstract provided.

The Greatest Integer Function, Alanna Rae

Journal of Humanistic Mathematics

No abstract provided.

Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa

Journal of Humanistic Mathematics

This review-essay on the mother-and-daughter collaboration Math on Trial stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.

Book Review: A New Index For Predicting Catastrophes: Poems By Madhur Anand, Joanne Growney

Journal of Humanistic Mathematics

This review explores Madhur Anand’s recent poetry collection from several points of view. One involves consideration of mathematical concepts and imagery in her poems. A second viewpoint takes into consideration Anand’s own field – she is a professor of environmental science with a focus on ecology. A third view considers the poems as art objects – words building pictures that offer to readers both insights and pleasures.

Fuzzy Logic In Health Care Settings: Moral Math For Value-Laden Choices, Sarah Voss

Journal of Humanistic Mathematics

This essay is intended as an example of “moral math”, i.e., ideas culled from mathematics which can positively impact social behavior. Specifically, it combines fuzzy logic with the ethical decisions which hospital staff and others are sometimes forced to make about health care (e.g., euthanasia issues following Hurricane Katrina). The assumption is that such decisions involve value-laden choices which lend themselves to “fuzzy” or “smart” protocols. The article discusses the history of fuzzy logic – what it is, how it is used, and how it might be even better-used as a support basis for making difficult choices …

Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig

Journal of Humanistic Mathematics

Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. …

Al-Khwarizmı And The Hermeneutic Circle: Reflections On A Trip To Samarkand, Asuman G. Aksoy

Journal of Humanistic Mathematics

In this paper we discuss al-Khwarzmi's life and aspects of his work and suggest a possible hermeneutic avenue into his contribution to mathematics.

Patterns Formed By Coins, Andrey M. Mishchenko

Journal of Humanistic Mathematics

This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non- overlapping circles. The first half of the article is an exposition of the two most important facts about circle packings, (1) that essentially whatever pattern we ask for, we may always arrange circles in that pattern, and (2) that under simple conditions on the pattern, there is an essentially unique arrangement of circles in that pattern. In the second half of the article, we consider related questions, but where we …

Combinatorics Of The Sonnet, Terry S. Griggs

Journal of Humanistic Mathematics

Using a definition of a sonnet, the number of basic rhyming schemes is enumerated. This is then used to discuss the 86 sonnets which appear in John Clare's The Rural Muse.

Connections, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Pythagoras Plays His Lyre, Sarah Glaz

Journal of Humanistic Mathematics

A poem about the Pythagoreans' beliefs and way of life.

Pension Building, Washington Dc, E Laura Golberg

Journal of Humanistic Mathematics

No abstract provided.

Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue

Journal of Humanistic Mathematics

The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students' conceptual understanding by creating an element of confusion, or "cognitive dissonance," in the students' minds using Jaywalking-style interactions in the classroom.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

A Meeting Of Minds: An Alternate Humor For Teaching Mathematics To Non-Stem Majors, Paul H. Grawe

Journal of Humanistic Mathematics

John Allen Paulos argued essentially for three forms of humor dear to mathematics: Incongruity, Gotcha, and Word Play. Unfortunately, these three are often combative forms and easily drive non-STEM majors out of mathematics and statistics.

William Dunham in The Mathematical Universe shows how a fine mathematician can use humor to draw non-specialists in. Central to Dunham’s success is his use of Sympathetic Pain humor, which creates softer synthetic Reconciler, Consoler, or Bridgebuilder humor styles.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.

The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam

Journal of Humanistic Mathematics

Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed …

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Kaleidoscopes, Chessboards, And Symmetry, Tricia M. Brown

Journal of Humanistic Mathematics

This paper describes the n-queens problem on an n by n chessboard. We discuss the possible symmetries of n-queens solutions and show how solutions to this classical chess question can be used to create examples of colorful artwork.

A Beautiful Proof By Induction, Lars-Daniel Öhman

Journal of Humanistic Mathematics

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

The Topology Of Absence, Nora E. Culik

Journal of Humanistic Mathematics

“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.

Geometry Of Life, Janice Dykacz

Journal of Humanistic Mathematics

Relationships in life can be expressed through geometric curves

Mathematical Double Dactyls, Tristan Miller

Journal of Humanistic Mathematics

No abstract provided.

On Mathematicians' Eccentricity, Robert Haas

Journal of Humanistic Mathematics

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.

A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look

Journal of Humanistic Mathematics

The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.

Mathematics: What Has It To Do With Me?, Man Keung Siu

Journal of Humanistic Mathematics

Mathematics teachers must have encountered the following question raised by students: “What is the use of mathematics?” Although the value of mathematics is not to be determined solely by its applications, to the general public this is a more important and more convincing facet of the subject. Nevertheless, this also brings up the corresponding query: is this subject being properly used? Does mathematics play a role in moral education?

On Similarities And Differences Between Proving And Problem Solving, Milos Savic

Journal of Humanistic Mathematics

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …

Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger

Journal of Humanistic Mathematics

We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).

My Finite Field, Matthew Schroeder

Journal of Humanistic Mathematics

A love poem written in the language of mathematics.