A Treatise On the Differential Geometry of Curves And Surfaces
The book A Treatise On the Differential Geometry of Curves And Surfaces was written by author Luther Pfahler Eisenhart Here you can read free online of A Treatise On the Differential Geometry of Curves And Surfaces book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A Treatise On the Differential Geometry of Curves And Surfaces a good or bad book?
What reading level is A Treatise On the Differential Geometry of Curves And Surfaces book?
To quickly assess the difficulty of the text, read a short excerpt:
In deriving them we refer the surface to a moving set of rectangular axes called the trihedral T. Its ver- tex M is a point of the surface, the zy-plane is tangent to the surface at M, and the positive 2-axis coincides with the positive direction of the normal to the surface at M. The position of the x- and y-axes is determined by the angle U which the tangent to the curve v = const, through M makes with the a^axis, U being a given function of u and v. In Chapter I we considered another moving ...trihedral, consisting of the tangent, principal normal, and binormal of a twisted curve. Let us associate such a trihedral with the curve v = const, through THE MOVING TEIHEDEAL 16T M and call it the trihedral t u . We have found (§ 16) that the varia- tions of the direction-cosines a', b', c' of a line L, fixed in space, with reference to t u , as its vertex moves along the curve which we call C u , are given by ds u P J d* u \ Pa tJ ds~ t„' where p u , r u denote the radii of first and second curvature of C u , and ds u its linear element ; evidently the latter may be replaced by VlUdu.
User Reviews: