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Word Choice in Mathematical Practice: A Case Study in Polyhedra

Abrams, Lowell and Elkind, Landon (2019) Word Choice in Mathematical Practice: A Case Study in Polyhedra. [Preprint]

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Abstract

We examine the influence of word choices on mathematical practice, i.e. in developing definitions, theorems, and proofs. As a case study, we consider Euclid's and Euler's word choices in their influential development and, in particular, their use of the term 'polyhedron'. Then, jumping to the 20th century, we look at word choices surrounding the use of the term `polyhedron' in the work of Coxeter and of Grünbaum. We also consider a recent and explicit conflict of approach between Grünbaum and Shephard on the one hand and that of Hilton and Pedersen on the other, elucidating that the conflict was engendered by disagreement over the proper conceptualization, and so also the appropriate word choices, in the study of polyhedra.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Abrams, Lowelllabrams@gwu.edu
Elkind, Landonlandon-elkind@uiowa.edu0000-0003-0513-2937
Keywords: mathematical practice, word choice, polyhedron, history of mathematics, philosophy of mathematics
Subjects: General Issues > History of Science Case Studies
Specific Sciences > Mathematics
Depositing User: Dr. Landon Elkind
Date Deposited: 12 Jun 2019 19:23
Last Modified: 12 Jun 2019 19:23
Item ID: 16104
Subjects: General Issues > History of Science Case Studies
Specific Sciences > Mathematics
Date: 9 June 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16104

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