By Luther Pfahler Eisenhart

ISBN-10: 0486438201

ISBN-13: 9780486438207

Created specially for graduate scholars, this introductory treatise on differential geometry has been a hugely profitable textbook for a few years. Its strangely specific and urban technique contains a thorough rationalization of the geometry of curves and surfaces, targeting difficulties that would be so much necessary to scholars. 1909 variation.

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Extra resources for A Treatise on the Differential Geometry of Curves and Surfaces

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When A = C = 0, k is indeterminate ; that is, when hence plane curves admit of an infinity of conjugates, they are the curves parallel to the curve. The other curve given only which has more than one conjugate is a circular helix, for since p and T are constant, A/C can be given any value whatever ; both the given helix and the circular helices conjugate to it are traced on circular cylinders with the same axis. 20, Tangent surface of a curve. For the further discussion of the properties of curves it is necessary to introduce certain curves and surfaces which can be associated with them.

Er =cZf -{- d^-i- dt?. This is expressible by means of (102) and (41) in the form (105) d

The segment of each tangent between the curves is of length c 1 Hence the involutes are said to form a 2

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A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart


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