%0 eBook
%M Solr-EB001230441
%A Tapp, Kristopher
%I Springer International Publishing
%D 2016
%C Cham
%G English
%B Undergraduate Texts in Mathematics
%@ 9783319397993
%T Differential Geometry of Curves and Surfaces
%U https://doi.org/10.1007/978-3-319-39799-3?nosfx=y
%7 1st ed. 2016
%X Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry.