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Foreword

from Geometry, Topology and Foundations

Marlow Anderson
Affiliation:
Colorado College
Victor Katz
Affiliation:
University of the District of Columbia
Robin Wilson
Affiliation:
Open University
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Summary

One of the most important aspects of geometry in the nineteenth century was the development of non-Euclidean geometry, and this chapter begins with two brief studies of aspects of its development. In the first, George Bruce Halsted reviews volume VII of Gauss's Werke and concludes from a study of many of Gauss's letters first published in that volume that Gauss's ideas on the subject had no influence on the independent discoveries of János Bolyai and Nikolai Lobachevsky, or on the earlier publication by Ferdinand Karl Schweikart (1780–1859). In the second article, Florence P. Lewis gives us a whirlwind tour through the history of the parallel postulate, from Proclus to Bolyai and Lobachevsky. She then proposes how this history, and its effect in how mathematicians understood the nature of a postulate, could affect the teaching of geometry in schools. In particular, she emphasizes that one reason for the study of geometry is its role in “training the mind.”

Another major aspect of nineteenth-century geometry was the development of projective geometry. That development began in the seventeenth-century work of Girard Desargues and Blaise Pascal, but, as Julian Lowell Coolidge notes, it then “dragged along” for about a century. In his article, Coolidge takes up the story in the nineteenth century, summarizing the work of such mathematicians as Jean-Victor Poncelet, Michal Chasles, Jacob Steiner, and Johann Karl Christian von Staudt. But then Coolidge remarks that by the end of the nineteenth century, the field of synthetic projective geometry was “pretty much worked out.”

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Who Gave You the Epsilon?
And Other Tales of Mathematical History
, pp. 113 - 114
Publisher: Mathematical Association of America
Print publication year: 2009

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  • Foreword
  • Edited by Marlow Anderson, Colorado College, Victor Katz, University of the District of Columbia, Robin Wilson, Open University
  • Book: Who Gave You the Epsilon?
  • Online publication: 26 October 2011
  • Chapter DOI: https://doi.org/10.5948/UPO9781614445043.014
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  • Foreword
  • Edited by Marlow Anderson, Colorado College, Victor Katz, University of the District of Columbia, Robin Wilson, Open University
  • Book: Who Gave You the Epsilon?
  • Online publication: 26 October 2011
  • Chapter DOI: https://doi.org/10.5948/UPO9781614445043.014
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Foreword
  • Edited by Marlow Anderson, Colorado College, Victor Katz, University of the District of Columbia, Robin Wilson, Open University
  • Book: Who Gave You the Epsilon?
  • Online publication: 26 October 2011
  • Chapter DOI: https://doi.org/10.5948/UPO9781614445043.014
Available formats
×