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1 - History of variational theory

Published online by Cambridge University Press:  23 December 2009

Robert K. Nesbet
Affiliation:
IBM Almaden Research Center, New York
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Summary

The idea that laws of nature should satisfy a principle of simplicity goes back at least to the Greek philosophers [436]. The anthropomorphic concept that the engineering skill of a supreme creator should result in rules of least effort or of most efficient use of resources leads directly to principles characterized by mathematical extrema. For example, Aristotle (De Caelo) concluded that planetary orbits must be perfect circles, because geometrical perfection is embodied in these curves: “… of lines that return upon themselves the line which bounds the circle is the shortest. That movement is swiftest which follows the shortest line”. Hero of Alexandria (Catoptrics) proved perhaps the first scientific minimum principle, showing that the path of a reflected ray of light is shortest if the angles of incidence and reflection are equal.

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Publisher: Cambridge University Press
Print publication year: 2002

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  • History of variational theory
  • Robert K. Nesbet, IBM Almaden Research Center, New York
  • Book: Variational Principles and Methods in Theoretical Physics and Chemistry
  • Online publication: 23 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511535161.003
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  • History of variational theory
  • Robert K. Nesbet, IBM Almaden Research Center, New York
  • Book: Variational Principles and Methods in Theoretical Physics and Chemistry
  • Online publication: 23 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511535161.003
Available formats
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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.

  • History of variational theory
  • Robert K. Nesbet, IBM Almaden Research Center, New York
  • Book: Variational Principles and Methods in Theoretical Physics and Chemistry
  • Online publication: 23 December 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511535161.003
Available formats
×