Elementary Mathematics from a Higher Standpoint. Volume III: Precision Mathematics and Approximation Mathematics

In Volume III, Klein explores the relationship between precision and approximation mathematics. He crosses the various fi elds 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 fi eld of abstract mathematics and properties that can be grasped by intuition. e fi nal part, which concerns gestalt relations of curves and surfaces, shows Klein to be the master of the art of description of geometric forms.