Science Networks. Historical Studies

A History of Folding in Mathematics

Mathematizing the Margins

Authors: Friedman, Michael

  • Provides a lucid exposition on the history of the mathematical concept of folding starting from the 16th century
  • Researches the various ways in which mathematical knowledge was and is marginalized
  • Surveys clearly the ways in which mathematical research and mathematical inference procedures were changing during the centuries
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  • ISBN 978-3-319-72487-4
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Hardcover $169.00
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About this book

While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised?

Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete.

In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

Table of contents (6 chapters)

  • Introduction

    Friedman, Michael

    Pages 1-28

  • From the Sixteenth Century Onwards: Folding Polyhedra—New Epistemological Horizons?

    Friedman, Michael

    Pages 29-91

  • Prolog to the Nineteenth Century: Accepting Folding as a Method of Inference

    Friedman, Michael

    Pages 93-112

  • The Nineteenth Century: What Can and Cannot Be (Re)presented—On Models and Kindergartens

    Friedman, Michael

    Pages 113-269

  • The Twentieth Century: Towards the Axiomatization, Operationalization and Algebraization of the Fold

    Friedman, Michael

    Pages 271-354

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-3-319-72487-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA in USD
  • ISBN 978-3-319-72486-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A History of Folding in Mathematics
Book Subtitle
Mathematizing the Margins
Authors
Series Title
Science Networks. Historical Studies
Series Volume
59
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-72487-4
DOI
10.1007/978-3-319-72487-4
Hardcover ISBN
978-3-319-72486-7
Series ISSN
1421-6329
Edition Number
1
Number of Pages
XV, 419
Number of Illustrations and Tables
92 b/w illustrations, 42 illustrations in colour
Topics