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About this product
- DescriptionThe calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, t the true moment of inception of the subject. It would t have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathemati- cians such as Zedorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have t done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Berulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are w hopelessly archaic. One by Robert Woodhouse appeared in 1810 and ather by Isaac Todhunter in 1861.
- Author(s)Herman H. Goldstine
- PublisherSpringer-Verlag New York Inc.
- Date of Publication18/10/2011
- Series TitleStudies in the History of Mathematics & Physical Sciences
- Series Part/Volume Number5
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight658 g
- Width155 mm
- Height235 mm
- Spine22 mm
- Edition StatementSoftcover reprint of the original 1st ed. 1980
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