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Physical Sciences and Mathematics Commons™
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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
Journal of Humanistic Mathematics
Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …
In Mathematics, As In Art, Andrew Granville
In Mathematics, As In Art, Andrew Granville
Journal of Humanistic Mathematics
The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?
Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield
Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield
Journal of Humanistic Mathematics
Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Journal of Humanistic Mathematics
Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Journal of Humanistic Mathematics
Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto
A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto
Journal of Humanistic Mathematics
Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.
As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …
Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala
Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala
Journal of Humanistic Mathematics
In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll's famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley's thesis and expound upon Carroll's artful use of symbolism to attack excessive use of symbolism in mathematics.
The Hamster Diaries, Pamela B. Pierce
The Hamster Diaries, Pamela B. Pierce
Journal of Humanistic Mathematics
When the pandemic hits, the author acquires a hamster, who provides some humorous anecdotes and some much-needed inspiration.
Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg
Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg
Journal of Humanistic Mathematics
In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, …