* Complete and unabridged presentation with recent advances and additional notes
* Annotations by the translators provide insights into the nature of science and mathematics in the late 19th century
* Each volume interweaves theory and applications
The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this a thorough and insightful account. Other volumes in this series include Introduction to the Kinematics and Kinetics of the Top, Perturbations: Astronomical and Geophysical Applications, and Technical Applications of the Theory of the Top.
In Volume III, Klein explores the relationship between precision and approximation mathematics. He crosses the various fields of mathematics – from functions in one and two variables to practical geometry to space curves and surfaces – underlining the relation between the exactness of the idealised concepts and the approximations to be considered in applications. Logical procedures are confronted with the way in which concepts arise starting from observations. It is a comparison between properties pertaining only to the theoretical field of abstract mathematics and properties that can be grasped by intuition. The final part, which concerns gestalt relations of curves and surfaces, shows Klein to be the master of the art of description of geometric forms.