1 - History of variational theory
Published online by Cambridge University Press: 23 December 2009
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 PressPrint publication year: 2002