Arts and Humanities Commons^™

Improving Equity And Education: Why And How, Patricia Clark Kenschaft

Journal of Humanistic Mathematics

Progress is possible. When I graduated from college, only 5\% of the new U.S. doctorates in mathematics went to women; now it is about 30\%. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and …

An Introduction To Fourier Analysis With Applications To Music, Nathan Lenssen, Deanna Needell

Journal of Humanistic Mathematics

In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for …

Galileo And Aristotle's Wheel, Olympia Nicodemi

Journal of Humanistic Mathematics

At the beginning of his last major work, Galileo tackles an old paradox, Aristotle's Wheel, in order to produce a model of the continuum that explains (at least to him) how line segments of different length could be put into a one-to-one correspondence. His argument seems like a playful digression. However, it is precisely this type of a one-to-one correspondence that he needs to support his work on free fall. In this article, we investigate how Galileo's model for the wheel paradox informs his work on free fall. We also examine some of the reasons his results on free fall---results …

The Taste Of Mathematics: Caroline Herschel At 31, Laura Long

Journal of Humanistic Mathematics

The poem brings to life how Caroline Herschel (1750-1848) learned mathematics from her brother William as they began to work as professional astronomers.

My Mathematics, Karen Morgan Ivy

Journal of Humanistic Mathematics

This poem reflects a personal kaleidoscopic perspective into a world of actively engaging others in teaching and learning mathematics.

Math Stories: Learning And Doing Mathematics Through Fiction Writing, Frederick Chen, Janna Raley

Journal of Humanistic Mathematics

In this paper, we advocate the writing of mathematical fiction (i) as an aid for students in learning mathematics, and (ii) to engage students in doing mathematics.

Three Poems: The Lorenz Transformations, Rotating The Strange Attractor To Find The Principal Components, The Sieve Of Eratosthenes, Robin Chapman

Journal of Humanistic Mathematics

No abstract provided.

Outlier, Or A Statistical Explanation Of Fear, Erika Dyquisto

Journal of Humanistic Mathematics

Postscript

As a seventh grader, I would sit in algebra class thinking I understood what my teacher had explained -- the order of operations or how to factor a polynomial -- but I would get home, try to do my homework, and my “knowledge” was gone. I had a vague idea that these formulas were about complicated relationships: the division and commonalities of beings. But just as I didn’t have the experience to allow me to discern the true nature of the human relationships these abstract concepts could represent, I didn’t know how to apply these new calculations to anything …

Poetic Reactions, Lawrence M. Lesser

Journal of Humanistic Mathematics

This trio of poems helps illustrate some of the many ways mathematics, poetry, and life integrate and inspire each other.

How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons

Journal of Humanistic Mathematics

A mathematical poem attempts to distill a mathematical concept and present it in a literary or visually compelling way. This paper presents an outline of my own personal method of composing such poetry. The outline is elucidated via an extended meditation on the composition of one particular poem.

Wandering About: Analogy, Ambiguity And Humanistic Mathematics, William M. Priestley

Journal of Humanistic Mathematics

This article concerns the relationship between mathematics and language, emphasizing the role of analogy both as an expression of a mathematical property and as a source of productive ambiguity in mathematics. An historical discussion is given of the interplay between the notions of logos, litotes, and limit that has implications for our understanding and teaching of Dedekind cuts and, more generally, for a humanistic notion of the role of mathematics within liberal education.

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …

The Mathematical Cultures Network Project, Brendan P. Larvor

Journal of Humanistic Mathematics

The UK Arts and Humanities Research Council has agreed to fund a series of three meetings with associated publications on mathematical cultures. This note describes the project.

Joanne Growney's Poetry-With-Mathematics Blog -- An Appreciation, Gregory E. Coxson

Journal of Humanistic Mathematics

Now is a good time to work on the boundaries of practice and theory, of art and science. We are seeing a rising tide of interest in these boundaries. Witness the growing Bridges movement, which has been exploring the connections between mathematics and the arts. Similarly, JoAnne Growney's blog, Intersections -- Poetry with Mathematics, explores the connections between mathematics and poetry. Through this review, I aim to give readers a taste of what can be found in Intersections as a way of encouraging others, be they mathematicians, poets, or neither, to visit the blog.

A Workshop To Introduce Concepts Of Moral Math, Sarah Voss

Journal of Humanistic Mathematics

"Moral Math" refers to the study of ideas drawn from mathematics which can positively impact moral decision-making and social behavior. This essay describes a workshop designed to introduce these ideas to interested individuals of varying degrees of mathematical and theological sophistication. Created by a retired minister and former math professor, the workshop details five sets of interactive exercises culled from game theory, theoretical complexity, fuzzy logic, basic algebra, and simple arithmetic. Exercises are user-friendly, interactive, and easily related by analogy to various social issues.

The Night I Almost Didn't Grow Up, Marion D. Cohen

Journal of Humanistic Mathematics

This is a short memoir about the role that math played in a certain part of my young life.

A Definition Of Mathematical Beauty And Its History, Viktor Blåsjö

Journal of Humanistic Mathematics

I define mathematical beauty as cognisability and trace the import of this notion through several episodes from the history of mathematics.

Report Supplement: Poetry Folder -- Selections From The Poetry Reading At Joint Mathematics Meetings 2012

Journal of Humanistic Mathematics

No abstract provided.

Raphael's School Of Athens: A Theorem In A Painting?, Robert Haas

Journal of Humanistic Mathematics

Raphael's famous painting The School of Athens includes a geometer, presumably Euclid himself, demonstrating a construction to his fascinated students. But what theorem are they all studying? This article first introduces the painting, and describes Raphael's lifelong friendship with the eminent mathematician Paulus of Middelburg. It then presents several conjectured explanations, notably a theorem about a hexagram (Fichtner), or alternatively that the construction may be architecturally symbolic (Valtieri). The author finally offers his own "null hypothesis": that the scene does not show any actual mathematics, but simply the fascination, excitement, and joy of mathematicians at their work.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Prove It!, Kenny W. Moran

Journal of Humanistic Mathematics

A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.

Excavation, Manya Raman Sundström

Journal of Humanistic Mathematics

No abstract provided.

Three Mathematical Lyrics, Lawrence M. Lesser

Journal of Humanistic Mathematics

The author shares three mathematical lyrics, debuted at opening banquets of MathFest, the summer national meetings of the Mathematical Association of America.

Logarithmic Spirals And Projective Geometry In M.C. Escher's "Path Of Life Iii", Heidi Burgiel, Matthew Salomone

Journal of Humanistic Mathematics

M.C. Escher's use of dilation symmetry in Path of Life III gives rise to a pattern of logarithmic spirals and an oddly ambiguous sense of depth.

The Day Without Evening: Leo Perutz, Evariste Galois, And Augustine, Andrea Albrecht

Journal of Humanistic Mathematics

The biography and historiography of Galois abound with conterfactual imaginations of how the course of mathematics would have been altered, had he not died so young. In the little know short story „The Day Without Evening,“ published in 1924, the Jewish-Austrian writer Leo Perutz essentially reiterates the usual narrative of the events leading to Galois‘ death, masked only by changing the name of the protagonist to Durval and transposing the setting to the Vienna of the beginning of the 20^th century. But he is also wary of such counterfactual imaginations. This can be understood in the context of Augustine‘s …

Numenrology: A Poetic Exploration Of The Lives And Work Of Famous Mathematicians, Mari-Lou Rowley

Journal of Humanistic Mathematics

No abstract provided.

Book Review: It Walks In Beauty: Selected Prose Of Chandler Davis, Edited And With An Introduction By Josh Lukin, Marjorie L. Senechal

Journal of Humanistic Mathematics

To paraphrase William Butler Yeats (with apologies), how can we knowthe edited from the editor?

Looking At Mathematics Blogs, Joanne Growney

Journal of Humanistic Mathematics

A mathematician, poet, and poetry-math blogger offers a personal selection of links to a few of the blogs and other websites she has found wandering the Internet.

Aesthetic Considerations In Mathematics, Nathalie Sinclair

Journal of Humanistic Mathematics

Drawing on some of the principles of humanistic mathematics first outlined by Alvin White, this paper seeks to examine the way in which value judgments are implicated in the growth of the mathematics discipline. After a short overview of some of the roles ascribed to the mathematical aesthetic historically, I turn to more contemporary positioning of the aesthetic in order to develop a framework that offers insight into the particular values, assumptions and desires that constrain what is done in mathematics, how it is done and why. My goal, at least in part, is to bring together under one umbrella …

Welcome To The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.